The most thorough way (if also the most time-consuming) is to map out your world's climates. If you have a proper climate map, stepping to biomes is fairly easy, but generating that climate map is itself a difficult task. You need a reasonably detailed altitude map at minimum, and if your planet is not "Earth with different geography" you also need to nail down a lot of nasty astronomical details. This is the sort of thing that researchers spend countless dollars on trying to do precisely (and still not quite managing it), so this is a hard topic. I don't have the many hours it would probably take me to do all the work for you, but I can give you a general process to form a good estimate of your planet's climates (and yes, the order of these steps is important, because generally each requires the previous step to be done):
- Develop your altitude map. This is the basis of generating your climates. The more detail you have, the better, but to-the-metre height measurements is overkill. At minimum, you need to easily separate these categories: deep ocean, shallow ocean (0-300m), lowlands, plateaus/highlands (~1000-2000m), and mountains.
- Map out your ocean currents. The basic rule here is that hot currents go towards the poles, cold currents to the equator. If you've done it correctly, you're going to end up with lots of circles and loops over the water; any current that's a dead end is a sign that you've probably made a mistake.
- Map out high-pressure and low-pressure zones. This requires two maps, as will most of the subsequent steps, one each for summer and winter (don't forget that winter in one hemisphere is summer in the other).
- Wind patterns come next. You'll need the pressure zone maps for this, and you'll end up with two maps once again; you might even want to draw the wind patterns on the same map. Winds blowing into a high pressure zone, across a mountain range (in the absence of an actual pass), or out of a low pressure zone, are signs that you're doing it wrong.
- Move on to temperature. This is a very tricky step that involves some guesswork, and you're going to need most of the previous maps to put this one together. Once again, two maps are necessary. Basically, you're going to divide your map into a few types of regions dictated by nearby ocean currents (or lack of them), utilize a temperature average based on latitude, and adjust that to match the differing conditions of those various regions. Hard-and-fast rules here are difficult, so a lot of this comes down to your own judgement.
- Precipitation is probably the ugliest step of all. Your maps for winds, ocean currents, and pressure zones will all be necessary here, and you will once again be making two maps. I don't even try to get actual measurements of rainfall: I just try to divide things up into general categories (none, low, moderate, high, extreme). To do that, I map out the major precipitation influences (namely: orographic lift/rain shadow, the ITCZ, and various wind patterns blowing from water to land like storm paths and the westerlies) and find how many are present in a given area to assign an appropriate precipitation rating.
- Climates are, after all of the previous steps, really quite simple. You take the precipitation and temperature maps (there should be four in all, unless your planet has no axial tilt and thus no real seasons), and for each point on your map you get summer and winter conditions of temperature and rainfall. Match those up against the climate classification of your choice (I favor the Koppen climates, nicely straightforward and widely used) and color in the appropriate climate.
For more details, such as how to actually go about most of these steps, I posted a thorough guide in an answer to a different question here, which I'm basically summarizing in my answer here and now.
Now, if you're just looking for a quick and easy set of tips, I can give you a few. If you have tropical conditions anywhere near tundra, and there isn't a 3000m+ altitude gap to justify the shift, that's an obvious problem. Tundra regions, in their warmest months, do not reach the coldest month in a tropical area. Snowfall in a jungle, for the same reason, is a giant writing error. Also, climates tend to change gradually, over a considerable distance. Two wildly different climates will not normally be found next to each other, barring a mountain range (the Andes, the Himalayas, the Alps, the Rocky Mountains, etc.) or other significant altitude change that can interfere with winds and rainfall dividing the two climates.