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Here you are: you are building your world, have come with a nice looking map for it, and now you are asking yourself if that map is realistic or if there is something you have overlooked.
And you want to ask us on Worldbuilding to help you with that. Here below are some of the points you need to check.
Tectonics and volcanoes
The total surface of a planet doesn't change because of plate tectonics. Therefore surface creation at divergent borders and surface destruction at convergent borders must balance.
Volcanoes can exist on both types of border: divergent borders tend to give more fluid lava and eruptions (see Iceland), while convergent borders tend to give more viscous lava and more explosive eruptions (Japanese, Indonesian volcanoes, for example).
Hot spots, like Hawaii, can exist in the middle of plates, just ensure that their migration on the plate is coherent with the shift of the plate over time.
Mountains and rivers
Tectonic plate boundaries decide where mountains are.. Rivers can have snow or glacier contributions, the origin of many rivers will be in the mountains. Rivers may also originate from places on the map with a lot of rainfall.
At the mouth of a river, variations in flow conditions can cause a river to drop sediment it is carrying. This sediment deposition can generate deltas, and sometimes islands. When there is no delta, a river mouth could become very broad before it reaches the sea, or consist of a narrow fjord, with mountains on either side.
Oceanic currents
Drawing up ocean currents is fortunately not that hard, as they follow some straightforward rules, but this example of Earth's currents will likely be useful. For this, you're mostly going to be using latitude lines, so make sure your map has those on it.
You start with two currents flowing westward near the equator (around 5N/5S). Whenever those currents hit a major landmass, they will be deflected north or south as appropriate towards the poles. They will generally go more or less straight at first, but at around 35-45N/S they will be deflected eastward by wind patterns; if they run into a landmass jutting out before then (see India), they will bend sooner. Follow them eastward on that latitude line (around 45N/S generally) until they hit land; generally, the current will split at that point into north and south currents (one going to the equator, the other heading to the relevant pole). There will be polar currents as well, flowing eastward at around the 60N/S lines.
The general rule with ocean currents is that they should always make closed patterns, typically circles; if you have a current that just stops at land with nothing continuing it, you've probably made a mistake. You might have to draw in some additional currents to have it make sense. Currents tend to run in force only through deep water; a continental shelf (which tends to be shallow for ocean water) might as well be the continent proper.
It's important to separate the currents by type (warm, neutral, and cold) for the later steps of making a world map, since these types have different impacts on local climates. Basically, currents heading towards the poles are warm, while currents heading back to the equator are cold, and everything else is neutral. It's entirely plausible to have a warm current at 70N/S (see the coast of Norway) and a cold current at 10N/S (see western Africa). A quick tip: the western coast of a continent tends to have a cold current when between 10-45N/S, but a warm current from 45-60N/S (reverse this for the eastern coast).
Wind patterns
To do an accurate map for an Earth-like planet, you will require separate maps for winter and summer for this stage. I'm going to refer to this as northern summer and northern winter, because the southern hemisphere will be in opposite seasons, but you can call them the hot and cold seasons or whatever else suits you. This is necessary because air temperature has a significant impact on these matters.
Part One: Air pressure systems. You can't make a useful diagram of the prevailing winds until you know where they're coming from, and that means knowing what areas will have higher or lower air pressure.
You need to chart the ITCZ line first. This is near the tropics and is a consistent low-pressure zone, but it does move slightly over the seasons. Draw a line at about 10N/S (whichever hemisphere is in summer) across the ocean eastward until you hit land. Your line is going to get pulled slightly towards the pole by continents, most noticeably on the eastern coast, but not too far; the strength of the effect depends on the landmass, and if the ITCZ hits the 20N/S line, either you've made a mistake or your map has something with the general size and placement of Asia. If you go past the tropic lines (23.5N/S), that's a problem unless you have a giant Pangaea in one hemisphere. Note that this assumes an axial tilt equal to Earth (23.5 degrees); adjust the axial tilt, and the suggested latitudes for the ITCZ will need to shift appropriately.
High-pressure systems are likely to form over the sea at around 30N/S in winter, generally on the eastern side of an ocean (near the western coast of a continent); in summer, move them to 35N/S. Overland, you only get high-pressure zones in winter; as a rule, a larger continent means higher pressure and a larger high-pressure zone (Asia has a monstrous zone in January). Smaller islands are effectively negligible in this section; overland refers to large continents, so something like Hawaii or Iceland has no meaningful impact.
Low-pressure systems in oceans tend to form around 55N/S in winter, and at 60-65N/S in summer; these will span most of the ocean at the relevant latitudes. Overland, they only form in summer; draw them mostly closer to the eastern coast, and once again a larger landmass reflects a larger low-pressure zone.
Part Two: Wind patterns.
Usually, wind currents flow from high to low-pressure zones, subject to the interference of mountain ranges and the like. They flow in a clockwise direction out of high-pressure zones in the south, but a counter-clockwise direction out of northern high-pressure areas: this diagram might be helpful. Low-pressure zones reverse this; northern zones generally have winds entering in a clockwise fashion, or counter-clockwise in the southern hemisphere.
High pressure zones will blow winds out in all directions, so you're going to be drawing lots and lots of arrows. Anything going towards the poles (>45N/S) will quickly shift direction eastward due to the westerlies. Winds blowing towards the equator will gradually be blown westward as they move towards the equator; these are the trade winds. For obvious reasons, mountain ranges will tend to block or divert winds blown into them.
Low pressure zones (including the ITCZ) will act like magnets, drawing in nearby winds, but it's quite possible to have wind passing between high and low pressure zones without entering either one if the rotation mentioned above results in the correct direction; if both zones are sending winds in the same direction, winds in between will likely be following that same direction instead of moving into the low pressure zone. This can also happen if you end up with a mountain range blocking the way, like the Andes.
Also make sure to draw the winds (following the clockwise or counter-clockwise rotation as appropriate) even inside the high/low pressure zones. These winds will be weak, however, if the zones are of significant size.
Temperature
This is a tough one. As with many other steps, you're going to need separate maps for summer and winter, as unless your world has no axial tilt, there's obviously going to be a big difference between January and June. Make sure your diagrams of ocean currents and winds and so on are on hand, since you'll be referring to them frequently.
First, map out some key influences. Ocean currents (warm/neutral/cold, as noted in that section) and continental influence are the relevant ones here; if necessary, get an extra pair of maps to track these. The current influences are coastal, and affected to some degree by wind; if your wind map has air blowing over the appropriate current type onto land, draw the relevant influence a little further into the land. Continental influence tends to fall under high pressure zones in winter, or low pressure zones in the summer; if you have something like Asia, expect its continental influence to be exaggerated near the center. Also, any ice pack situations (see northern Canada and Russia) will be continental as well, since the water moisture isn't really accessible.
For the temperature guides, I'm relying on these images (source is from this excellent tutorial):
The latitude guides are a general pointer for temperatures at a given latitude, assuming sea level; temperatures will drop roughly 6C for every 1000m of elevation, so mountains will be significantly colder. The last image is a color guide relating the colors in the latitude guides to the appropriate temperature ranges. Continental plus, essentially, is to be used in a central-Asia type of area, so it's not relevant unless you have large continents with probable ice-packs blocking the north or south.
Be warned that these guides aren't exact (climates being by nature rather inexact when trying to apply what amounts to educated guesswork), so there's a fair bit of fudging involved. Coastal areas tend to have milder temperatures (warmer in winter, cooler in summer), but this doesn't typically apply to inland seas or ice-pack conditions. If you're using the extreme edges of the scale (dark red or purple) in more than very small areas, you'll probably want to do another draft; applied to Earth, this method maps the greatest heat only to small parts of Africa and Australia, whereas the nastiest cold is only in Antarctica or Siberia, or perhaps something like Everest.
A warning here for complex worlds: this assume Earth-like conditions. Changing the axial tilt, the solar constant (essentially the relation between average orbital distance and the sun's luminosity), orbital eccentricity, albedo, and so on will have a serious impact on the latitude guide. Adjusting the latitude guide to match changes in these parameters is probably a matter of educated speculation, but I'll try to give a few pointers. Changing the axial tilt will have a greater impact at higher latitudes; a larger tilt translates to greater extremes in temperatures. If solar luminosity or orbital distance changes, that will affect your planet's average temperature.
A non-trivially eccentric orbit (I would think e <= 0.03 would be trivial, but that's just my opinion) poses particular difficulties, since orbital distance will not remain effectively fixed. This obviously will affect temperatures and probably require you to make separate latitude guides for the north and south hemispheres as well as for the seasons; you'll also need to place perihelion and aphelion in relation to the seasons. The likely result is doubling the number of diagrams you'll have to make, as the guidelines around summer and winter will be different for each hemisphere.
Precipitation
This one is possibly the single ugliest topic (being the most subject to estimation and interpretation), so you should expect to do multiple drafts before you get this right. This is essentially going to be painting a lot of influences, and then estimating total precipitation based on how many overlap at any given area.
Make very sure you pay attention to wind direction; a lot of these factors change drastically if wind is blowing onto shore versus being parallel to it or from land out to the ocean (the former scenario results in more precipitation, while the last one likely means none). Note that a mountain range will, under most circumstances, block any significant rainfall on the other side unless precipitation can come from both sides. Also, inland seas will generally not offer significant material for precipitation, although unusual circumstances might come up; North America's Great Lakes, for instance, have occasionally been the source of truly alarming blizzards.
Start with the ITCZ line; check your wind map if you don't remember what this is. This one is a huge influence, because it draws any winds coming from the equator and more besides: it effectively is worth double any of the other influences. It's not quite a guarantee of massive rainfall, it must be noted: the Sahara sits under the ITCZ for half the year, yet it's a desert; to my understanding, this is because the Sahara is too hot for any moisture to really precipitate, no matter how much evaporated from the Mediterranean. Still, this is where the great majority of tropical rainforest is going to turn up. Paint a reasonably thick line (around 10 degrees of latitude) over the ITCZ, and expect a lot of rainfall over this area unless you get a mountain range or something like that in the way.
Next come some effects from westerlies. This starts at around 30N/S in winter (moving poleward), or around 45N/S in summer, and is mostly present on western coasts. You'll get a fairly strong effect on the coast, but it quickly weakens. Winds can carry the effect a long ways inland if blowing in the correct direction, but rainfall will diminish over distance; for any map with an Asia-like continent, it's likely to end up with a desert near the center.
Storm paths are another influence. These are mostly on eastern coasts from 25-50N/S, and are found west of high pressure centers over oceans. These bring a lot of precipitation several degrees of longitude inland if the winds blow directly onshore and still quite a bit even farther inland, but like other influences this one diminishes with distance. As the name suggests, you may want to note these areas as being storm-prone; the best examples of this on Earth are the eastern coast of the U.S.A and the Caribbean, with the hurricanes that so often roll through.
Orographic lift, also known as rain shadow, is another crucial point to take note of. If rain-filled winds get blown onto mountains, the clouds will rise. As they rise, they get colder, and the moisture condenses and falls out of the sky: when they descend on the other side, they warm up again, so any moisture left is unlikely to precipitate. The end result is a lot of rain on one side of the high ground but very little on the other. This is what gets you temperate rainforests like southwestern Canada has, and it's also why plateaus like Iran will generally be dry. The greater the elevation change, the stronger the effect; a mountain range will be more significant than a plateau.
It is crucial to note that ocean currents may play a role here. If you have a cold current near a high pressure zone, any winds blowing onshore over cold currents are very unlikely to lead to precipitation, even if orographic lift would normally occur. This leads to areas like northwestern Africa, which has almost no actual precipitation.
As a general rule, precipitation drops as you move towards the poles; high pressure zones also tend to have reduced precipitation, due to winds rushing out of them instead of into them. Temperatures are notable for certain cases: if you have a sudden rise in temperature, you probably won't get much precipitation. Winds blowing from polar regions are likewise improbable bets for any real precipitation.
Climate zones
This is what you're ultimately working for, if you've gone through all the previous steps, and it's almost anticlimactic that the final step is actually one of the easiest. Take your temperature and precipitation maps (there should be four in all, since you need summer/winter maps for both) and correlate the data at given regions to find your climates; I would recommend the Koppen climates for classification.
I don't think it necessary to spell out all of those climates in detail here, but be warned that your precipitation map is only an approximation and should be used as such; think of precipitation in terms of low, moderate, high, extreme, etc., rather than in exact measurements. If you've got a tropical region that's drenched in one season and bone-dry in the next, for instance, you probably have a savannah climate (Aw or As). If you're not reaching at least moderate precipitation in either summer or winter, you have steppes or a desert (the B-range climates). Coastal regions outside the tropics will almost always be temperate (the C climates) unless you're in the polar regions, as the ocean is a powerful moderating influence on temperatures. Regular snowfall does not automatically mean a continental climate (the D climates), since cold days happen even if the monthly average is above 0C, but lingering snow that sticks around for a few months is another matter.
Cities location
tbd
Story-dependent information
Other information on a map will depend on your story. If there are political angles, there will be some boundaries involved, like country borders.. resources.. and in case of a war: front lines, army strongholds, castles, fleet base.
A tip.. since februari 2022, there is a guide website for fictional maps online, with directions and lots of tips and software tools https://rocketexpansion.com/fantasy-world-building-maps/
Just going to chime in on this.
Your world will seem realistic enough if you just get a globe and look for actual land and corresponding weather on the real Earth, and then copy it. If you want island settings, look for chains of islands, and understand what formed them.
If you want a tornado alley, copy Oklahoma. Find your livable soaring mountains, look to the Rockies or Andes.
If you want deserts, look in the American southwest, the Sahara, and elsewhere.
A black sand beach, you can find it in Hawaii. Vast forests, there are several rain forests available.
All natural world examples are based on Earth; you can pretty much cut and paste the elements together, if you include their transition-to-something-else areas, and be good enough.
99.99% of readers are not climatologists, they aren't going to lose immersion in your story because for plot purposes you put the rain forest on the wrong side of the mountain. They won't even notice.
Just copy some answers from the real world and you'll have done more than most authors.
I needed an imposing cliff for a story, I just googled "tallest cliffs" and found Biggest Cliffs In the World. I checked out the conditions, my story was indeed shore-adjacent, I picked a mile-high cliff and transplanted it to my shore. Were the wind and currents and soil and rock composition right for that? Beats me, I did not mention them; it was just a sheer cliff of a few thousand feet I needed for dramatic purposes.
World building can be a fun game and hobby in it's own right, but it isn't 'writing'. The world, consisting of nature and culture, is there to be an antagonist or an ally to your heroes and villains; to provide conflict or advantage for either one.
If what you want to do is write, then build the world as you build your plot, considering it an antagonist, or an ally, or (not too often) a neutral element for your characters. Like any character, always consider the nature and culture of a scene; the world has a role to play here too.
In my opinion, the time spent world building for the fun of world building is not time spent writing. I cut and paste my world elements from the real world, and build my world to suit my specific plot, not as a canvas for a dozen stories. If I have done a decent job, I am able to build more plots that fit into it, and perhaps make some use of the less specific areas of my map.