This method take a long time, but it will work.
First thing, dig out a living space and get your farms going. Unless you brought tons of food and drink, you will use up your provisions before you can get past the aquifer.
Chop enough trees to make a carpenter workshop, use it to make wooden blocks, wooden pipe sections and wooden enormous corkscrews.
Turn on Architecture labor on all your dwarfs, and turn on pumping labor on everyone except the miner and carpenter.
Build 2 pumps side by side, dig a channel in front and behind them. The water will be pumped out of both tiles. this gives your carpenter a space to stand and escape from after he builds a wall in the adjacent square. Once thats done, disassemble the pump in front of the newly created floor and rebuild it down the row, make a new channel. Continue until you have a row of wooden walls imbedded in the aquifer layer. As long as you only work on 2 channeled tiles at a time, and both are being pumped out, you will have very few suspended wall constructions.
Once you think I've gone far enough, turn your operation by 90 degrees and continue. then another 90 degrees , etc until you complete a full circuit. DO NOT channel out the center tiles until you are placing the very final wooden wall in the circuit.
If the aquifer has multiple layers, do the same thing, but instead of pumping the water into a channel, you have to keep a pump on the upper level to dispose of the water. Its the only way to get rid of the water once you are nearly complete.
I've managed to get through 2 layers of aquifer with this method with as small as a 4x4 top hole and a 2x2 lower hole. Its very delicate, if you channel the wrong place, you can screw yourself. Rule of thumb is to never channel out the middle tiles until the perimeter wall is one block from being finished. It can be done, but I literally spent 20 minutes real time resuming suspended construction. there was too much water spawning. You want as little surface area as possible for your pumps to work against, every channel you make increases the amount of water produced. On the 2nd layer, you will spend a lot of time constructing and deconstruction walls and floors to control where the water can go. Also, Do not dig out the corners. aquifers don't produce water diagonally, but water can flow diagonally.