As was suggested initially, the best way is to make a screw pump, which you can do entirely from a carpenters shop out of wood parts if you're just gonna use it to pump water.
A
screw pump (b->M->s) setup I use usually looks like this..
wwwwww
wwwwww <--- (w)ater surface
..p... <--- (p)ump
.WpW.. <--- (W)alls (constructed)
.WvW.. <--- (v) channeled out (creates an up ramp on lower level)
.WWW.. <--- (.) presumably surface/grass
wwwwww
wwwwww <--- (w)ater underground
...... <--- (.) unmined area
......
..^... <--- (^) up ramp
.. ... <--- ( ) mined area
.. ...
<farm> <--- opens up to your planned farm (mined out already, and preferrably closed off from your fort with doors).
you have the TOP of the river or pool water source, and then, with two tiles between, you want to channel out the ground. You need to construct some walls around the channel so the water doesn't just spray out everywhere, but instead is trapped and goes down the channel. You also need to construct the pump so that it pumps in the correct direction. Once everything is built, have a dwarf (with pump operating labor enabled) go pump water down. You need to watch the farm fill up with water, because pumps work VERY fast .. as soon as you have enough water, stop the pump and then wait for the water to evaporate/get to 1/7 level everywhere.
Making a pump requires 3 parts:
blocks (wooden from carpenters shop)
gigantic screw (wooden from carpenters shop)
pipe section (wooden from carpenters shop)
When you're done flooding your farm with water, you can construct a wall (b->C->w) in the couple of mined out areas between the ramp and the farm so that no creatures can fly into your fort through the hole.