40d:Irrigation

Dwarf Fortress uses realistic water dynamics, including measures of depth. A depth of 7 is full, depths of 1 will evaporate, leaving the stone wet and thus suitable for farming. Your goal in irrigation is to get a section of ground to be 1's.

The reservoir method involves building a small reservoir between two floodgates and a farming chamber at least 7 times as large as the reservoir. a reservoir of 10 tiles, for instance, can water a 7x10 chamber effectively. Water is let into the reservoir by lowering, then raising one floodgate. The other floodgate then releases the water into the farming chamber. It spreads around, then evaporates after becoming 1 deep.

Oldschool Style

1. Dig from the farm plot to any source of water, but keep a single tile of wall between the newbuilt channel and the water. Also, dig a passage from the plot towards lower ground that'll serve as the water drain.
2. Build a door or floodgate, and three mechanisms.
3. Place the door in the channel. The idea is that it'll block the water from coming through when closed.
4. Build a lever and link it to the door or floodgate.
5. Pull the lever so the door opens. Send a miner to dig that last wall keeping the water from rushing in.
6. Ideally, here the miner will run like hell. The water is actually fairly slow.
7. Use the lever to close the channel once you feel you've got enough water to spread over the area.
8. Wait for water to drain out to at least 1/7 per tile. You can use grates and hatches to speed up this process.
9. Make farm.
10. Profit!