In my story I want to create a post apocolyptic scenario where a good deal of the Earth's water has been evaporated or simply drained. Leaving a vast desert. There are suvivors that are attempting to rebuild cities on he surface of the planet. This can be a very long time after whatever cataclysm took place for believabilitiy. There is still roughly 10-20% of the planet covered with water.
This is an "I want X to happen, but I don't want to deal with the consequences of X" question. Anything that would evaporate that much water would devastate all life on earth. Nothing man can do (today) can do that. So, let's look at a natural possibility, no matter how fantastic.
The water needs to go somewhere inaccessible. The only place it can go is down. Can we super-charge the aquifers? How about a geologic/volcanic event that pushes land up and draws water down? Open a big enough hole (a whomping huge hole...) and the oceans would fill it. Of course, geologically, over time the pressure of all that rock atop it would eventually squeeze the water back to the surface.... but that would take a very long time. (A nice ending to the story, someone watching the first spring appear. You could create a religion based on that experience.)
Frankly, your biggest problem is how people survive. Water=life. If you haven't read Frank Herbert's Dune you should. It's primary plot element is a desert planet and how people survive on it.
As comments and others have said; the water has to go somewhere, and there is no place on EARTH for it to go. In the spirit of "draining", have it drained to space. By aliens, or by Humans abandoning the planet and taking their water with them. Maybe because the world is polluted and the oceans are dying, and here comes Global Warming, or whatever. Aliens with anti-gravity tech would be your best bet, that is an awful lot of water to transport into space and move elsewhere.
But perhaps aliens have decided they will be colonizing Venus, which has a temperature and proximity to the Sun (better for collecting solar energy) more to their liking. But they will be terraforming it and need the water from Earth so they take it from the primitive humans without warning, defeating all the human defenses, attacks and atomic retaliation like swatting away flies. They do not respond and kill us, they just ignore us. But they drain the oceans and don't bother with fresh water lakes and such; it isn't worth their effort when they can (using anti-gravity) vacuum up the Pacific and Atlantic. And they don't take all of those; they only take what they need.
In any case, somebody takes most of the water, and most of the people and animals with it (95% would be dead anyway). They leave behind all the giant fresh water lakes and inland seas. Civilization has collapsed and nobody knows WTF is happening on Venus. It can't be good! But the people left still have to live and eat after the robbery; so your story ensues.
P.S. If you want; they can take all the salt and minerals from the oceans too; there are thousands of compounds they might want there that would be absent on hothouse Venus. So they leave behind freshwater oceans. Find a contour map of the oceans with depths; pick your new ocean level and you will have your new landscape.
This probably isn't the style of "desert" you are imagining, but a snowball Earth scenario could do this. While the water would technically still be there, it would be locked up in miles thick ice sheets and be largely inaccessible.
The only other semi-realistic scenario is for solar radiation to break down water and the hydrogen to escape into space (basically the Mars scenario.) But this would take a crazy long time and would require a significant weakening of Earth's magnetic field (and therefore the core dynamo) which might not happen before the Sun heats up too much for Earth to remain habitable, but most people wouldn't know that.
Most of the answers here are talking about hiding the water, but if you truly want it to disappear, you would have to split it apart.
Water is $H_2O$, meaning with enough energy you could indeed split it into hydrogen and oxygen, as per the equation $2H_2O \rightarrow 2H_2+O_2$. The problem is that this reaction requires a huge energy input, as well as a conductive medium. You'd also have to worry about all of the flammable hydrogen gas and oxygen you would be producing all at once. If that doesn't blow up the earth, it'll certainly change the composition of the atmosphere.
If you were to zap the oceans (which are able to conduct electricity, unlike freshwater sources) you would be hosting the biggest fish-fry the world has ever seen, and would decimate all oceanic life. I would certainly think it would be impossible to concentrate that much energy in one place, but hey, if someone felt like making a doomsday device, I guess they could try (why they would want to, though, is beyond me
maybe some bad sushi)
What you'd be left with would be an absolutely uninhabitable planet. The oceans have a huge thermal mass, meaning they can absorb immense amounts of energy while only slightly changing in temperature. If we lose that thermal mass, we would see crazy temperature fluctuations and unstable weather patterns.
As well, most of the reactions on which all life depends occur in water. Those organisms which tolerate extreme dessication (think seeds and fungi) are usually in a period of stasis until they find water again. This means even life forms that are adapted to a dry environment will basically hit pause until dry earth gets its shit together.
Also, the primary feature of water which allowed earth to become survivable is the fact that ice is less dense than water and floats. This creates an insulating layer on small bodies of water, which allows life to overwinter at the bottom. If there were no bodies of water, most aquatic and amphibious life wouldn't last the winter.
Your scenario does allow for ~10-20% of the earth's water to remain, so there would probably be some pockets where life still exists. These oases would still have to contend with the massive-scale disruption of ecosystems and food-webs on which they rely, so they would need to re-equilibrate to their new environment. With such strong selective pressure, you would likely see what few life-forms still exist quickly evolve in dramatic ways. Since these pockets are few and far-between, there wouldn't be much genetic drift, leading to heavily inbred populations with a bunch of weird recessive traits.
In summary, you don't have to hide all the water, but you'd need loads of energy to make it all go away. Assuming you'd be able to pull off such a massive feat of water-dissappearance, you would be left with broad swaths of entirely uninhabitable wasteland peppered with a few oases of vastly different organisms and violently unpredictable and extreme weather patterns. Humans would most definitely only be able to survive in these pockets of life, but agriculture as we know it would probably be impossible, since the air would be much drier than it is today. They might be farming dry-tolerant fungi or something, surviving on mushroom jerky.
You don't necessarily have to strive for ultra-realism, (if you did, I think the world would just cease to be) but hopefully this might give you some ideas about where you want to go with what you've got.
Is this supposed to be realistic science-fiction, or can it be fantasy or handwavium-alloy science-fiction? In centuries past, natural philosophers tried to explain the biblical Flood using physical mechanisms (see for example Noah's Flood: The Genesis Story in Western Thought by Norman Cohn); what you're asking for is basically the same problem in reverse (there's too much water on Earth for it to disappear like that).
One theory was that the Earth's interior was filled with large flooded caves which served as water reservoirs, which when perturbed somehow spilled their contents on the surface ("all the springs of the great deep burst forth", Gen. 7:11). If you're willing to go with Bible-based mythology "explained" in this way, you could reverse the mechanism and posit that great caves inside Earth's crust, which were empty so far, have just collapsed under the ocean floor, and most water has drained into them. Cue cataclysmic storms as millions of cubic kilometers of water are turned to steam. This is of course totally inconsistent with our current knowledge of Earth's geology, but yours doesn't have to be exactly our Earth.
There is a way to do this, but it involves moving forward in time 500 million years into the future when the solar constant has increased enough to start the process of evaporating the oceans.
Briefly, as the hydrogen in the Sun's core fuses, helium "ash" accumulates in the core. The radiative energy of the fusion reaction more or less balances the gravitational pressure of the sun's mass, but the fusion fuel in the core gradually depletes. The gravitational pressure increases as the fusion reactions slow down, increasing pressure until the conditions are met for Helium fusion. This is a much "hotter" and faster process, so the sun becomes brighter (and larger).
Dramatic sunrise in the year 500,000,000 AD
On Earth, the temperature increases to the point that the stratosphere becomes saturated with water vapour, at which point the intense ultraviolet radiation breaks the water into hydrogen and oxygen, and the hydrogen escapes into space. From 500 MY to 1000 MY, the process continues until the Earth becomes literally bone dry and biological life becomes impossible.
Of course this makes for some difficulties in your story, since after 500 MY, humans will have evolved into post-post-post-post-post^n humans, and it is hard to see what sort of story will be written about essentially totally alien beings on a very alien planet (totally alien biosphere etc.) If you want Earth people to be the heart of the story, they will somehow have to be brought into this time period. They could be advanced via some sort of artificial or natural wormhole, or even recreated as some sort of performance art project by the AI who inhabit the Solar System in that era.
Of course they will have some serious adaptation issues (outside of the obvious lack of water, there will be very little CO2 left in the atmosphere due to the high temperatures interrupting the carbon cycle and plant life as we know it becoming extinct, and the rest of the biosphere will have evolved over millions of years to adapt to the arid conditions, which will make the Gobi desert seem like the ideal setting for a beach resort).
Earth between 500-1000 MY in the future
The other issue which may be faced is after 500 MY, much of the Solar System will have been industrialized and reshaped by our descendants, so planets may have been moved, the Sun may have been modified by "Star lifting" and artificial gas giants now orbit the Sun carrying the excess hydrogen mined in ages past, and of course the entire sky is now dominated by the structure of the Matryoshka brain where the post human AIs reside.....
The real civilization is here
Elaborating on Gene's answer.
You know how the oceans would rise if the polar caps melted? The reverse is true: when the Earth cools, the polar caps draw water from the oceans.
A lot of land that is underwater today was not so during the last ice ages. Not only that... Since polar ages change the whole cycle of water on the planet, many rivers cease to exist whenever we enter one.
So there you go. What you need is an ice age. Mankind can do one, with nukes (but the how's of that are a topic for another question, in another site).