Depending on the size of your fortress, you might only need, say, 48 levers if you have 256 rooms. This is obviously much better than having 256 levers for each water trap. The way to do it is pretty simple: at the top of your fortress, make sure you've got 2-3 Z levels for water canals. The reason for this is that water will drain faster if it has more water on top of it. 2-3 Z levels of water pressing down will flood any room quite rapidly. Don't put any water on this level yet. Just dig out some canals to get to each shaft, and make the canals tall enough to get rapid water flow.
You should dig shafts that pass through each major room on every floor. The water will be going from the canals at the top, then down these shafts then into the rooms that they pass through.
Let's say you have 8 shafts. At the top of each shaft, where the canal is, you should have a hatch with a lever connected it. Place the levers so you can remember which one controls which shaft. You should now have 8 levers. Place a hatch on every floor in every room that the shafts pass through, to stop water from going to the floors below. Next, for every floor in your fortress, build one lever, and connect it to all of the hatches on that floor. You should now have another 8 levers, and it would be convenient to put them in a line. Set all of these levers to be on, so that the hatches on every floor are open.
Next, around each of those hatches, build floodgates. You want to make sure that no water accidentally gets into the wrong rooms. You can skip the floodgates if you want to, but I strongly recommend them for safety and convenience. Again, build one lever for each floor to control all of the floodgates on the same floor. Leave these levers off by default. It would be convenient to put them in a line next to the levers for the hatches.
You should now have 24 levers, and you should be able to flood any of 64 rooms.
Finally, at the bottom of your fortress, place a drainage system. Again, 2-3 Z levels is ideal for rapid water-flow. It's better to make your drainage canals taller rather than wider. Remember that once you find mushroom caps and other underground trees, you'll start to get trees clogging up your water systems because the ground is muddied. Build roads in every spot where you don't have hatches - this will also help you get rid of some of that useless stone lying around.
Once you've got everything else ready, you can connect your top-level canals to any infinite water source. Remember to use roads, and remember to make your canals tall, not wide. It should go without saying that every room with a water trap in it should be made water-tight with doors that can be forbidden as you need.
Now you're finished. To flood a room, you start by opening the floodgates and closing the hatches for all rooms on that floor, and then you open the hatch for the shaft that passes through the room you want to flood. Closing the hatches will ensure that the water cannot go beyond that floor. By keeping the floodgates closed on every other floor, you ensure that no water will get into a room accidentally, so you minimize the amount of mud you need to clean, and keep the chance of accidental flooding low.
When the room has flooded, and the creatures inside are dead, you can close the hatch for that shaft and open all of the hatches for the rooms on that floor. The room you flooded will dry out soon enough, and then you can close the floodgates for that floor to prepare your flooding system to be used again.
You can use this in a lot of different ways. If you're running a fortress with Spread Contamination on, you can use this like a toilet's flush mode to clean dirty rooms before they spread vomit everywhere. If you want to, you can temporarily move all of the dwarves to some safe location and wash the entire fortress. If you set these traps in hallways, you can use them to drown invaders both from below and from above. Naturally, it's also quite useful if you want to give your nobles some time to enjoy a little mist - just make sure they don't suffer an unfortunate accident. You might have to mur... um, err... keep them safe by closing the hatches on their floor, so they don't fall down the water shaft. For added, umm, safety, you might want to lock their doors to make sure that nobody bumps them.