i'm assuming you have a limitless supply of wood, and enough components for at least 2 screw pumps (4 is prefers)
no power required, althou it can make it easier)
and that you have more the 1 layer of aquafer to go through (1 is easy, just 1 pump line wall build staircase))
it can be done using just 1 pump operator for all but the last level, then I'd recommend getting 2)
i relied on the fact that aquifers not only generate, but can also absorb limitless amounts of water)
and that aquifers don't generate water in diagonal squares.
make a 4 by 4 square above the aquifer.
channel out the 4 corner. build a pump between 2 of the holes.
one hole is being emptied and the water drains away into another.
if you look on the first aquafer level you now see this (just portraying 1 corner)
x=rock
r=ramp
xxx
xrx
xxx
order one of the 4 sides to be mined, and build a wall there out of wood. (if you can smooth the walls that's even better and quicker, but in soil you cant)
after 3 or 4 cancellations (less if the carpenter is any good) the wall is built, and you move on the the next side. (which will have fewer cancellations)
build op 3 of the 4 sides, and leave 1 side open facing another corner.
x=dirt
r=ramp
w=wall
xwxxxx
wrxxrx
xwxxxx
mine that out and line the 3 sides (on the inside 4 squares you can also make a up/down staircase all the way to the next aquifer level to help with drainage, but this can cause trouble for the last aquifer level, i only used 1 of the inside blocks as staircase instead of all 4)
when done on the first aquifer layer it now looks like this
x=dirt
r=ramp
w=wall
o= open space
xwwxxx
wrowrx
xwwxxx
in this case we now move the pump (above here) to the hole to the right, and build up the 3 remaining sides there.
then remove the in between wall, and then mine out and build a wall for each of the 2 remaining dirt walls. you then have this
xwwwwx
wroorw
xwwwwx
you could now already build a pump down here have move on to the 2de layer.
if you have only 2 layers you can already break through now. build the 4 walls in the 2de aquifer layer and then build a staircase and channel down.
if you have more layers then you can now continue to build this moving on the next hole moving the pumps around as appropriate.
connecting the last bit is a bit tricky as you now have nowhere to pump the water.
wall off one of the corners you wall up earlier, remove one wall facing a dirt layer and you now have a place to pump water into again, that you can fix later quickly without causing to much spillage
ita wise to have at least 1 drainage to the a lower aquafer level when you do that thou, just in case things take longer then planned. and if you're on the last level of the aquifer make sure you dig down have a wide open space down below for excess water to evaporate (i was left with only 9 patches of mud when i did this).
once you go all the way around, build a stairs in the centre, move the pumps down and channel out the 4 corners again, rinse repeat.
as long as you keep the number of open aquifer wall as low as possible you should be able to to this without too many cancellation, specially as your dwarfs learn to swim.
just some general tips.
- make a burrow of the working area and assign the proper dwarfs to it so they stay close,
- make a meeting hall close by, and keep some food and drink handy too.
- and of course make a wood stockpile close by and a place to store pump components for quicker rebuilding.
- always get the pump as close to your working area as possible, plan ahead so you can do this.
if you have enough power you can move the water upwards and out of the hole without any risk of spillage when connecting the last corners of course. just make a 5th channel on top to drain it into.
hope that helps (and its at least somewhat clearer then mud). just used this technique to go through a 3 layer aquifer in 3 seasons, without spending all my time on it.
no overly quick, but pretty doable.
p.s. someone posted this technique earlier somewhere (in a somewhat shorter description), credits for the idea go to him... if only i could remember who.