There is a pretty good writeup on the wiki but basically it involves having two plugs that you can drop separately. You have one outer ring that you carve out of stone and drop first into the aquifer and an inner ring that you can use a scaffold to hang in the air until you are ready. After you drop the first ring you have to go down and pump out the water from within the ring so you should have the first layer blocked by the outer ring and a central area that is pumped out. Then you dig out the center and drop the inner ring (which really can just be a plug) and then dig down into that.
You need one 'ring' for each level you want to get through (beyond two and it gets unmanageable), and I have had it 'not work' even when it should have and cannot explain it.
From my personal experience (I almost always embark with aquifers) I have found that in the past when you could see how many layers you have the 'plug' method (dropping the chunk of ground in) is fastest and easiest, for anything more then one however the pump method is fastest and best. In the newer version where you cannot see how deep the aquifer is I use the pump method each time. The plug/ring method requires you pre-build the amount of rings needed to do the job, so if you don't know how many levels there are you have to guess. Build too many rings and you wasted time, build too few and your work was for nothing.. The pump method however can work as many times as you want (though it is more of a hassle in general), plus no giant hole in the middle of your ground