Well what you'd like to find is a one-layer aquifer. On the map, more than two aquifer layers can be tougher.
There are several fun tricks with cave-ins or magma or ice, but using pumps is fairly easy once you figure it out.
It is exactly 1 layer of stones that produce water on all squares adjacent to them. So the ideal way to get through it is to have a stairway going through the layer, with constructed walls surrounding the stairway to keep it dry. If you extend the stairway one more level down beyond this, and avoid building back up into the aquifer, no water will ever get into the fort.
The other secret is that aquifer tiles also
absorb water. If you set up a pump to take water and push it into an aquifer, it will suck up the water. So on the layer above the aquifer, you dig down your stairways based on speed faster than the water fills up. After that, you channel out an area around the stairs, where you intend to build your wall. Don't worry when it fills up with water.
Build pumps to pump the water from the places where the walls will go, you can power them by dwarf power, no need for windmills. Then channel out the output square for the pumps. As I said before, this will mean the water spits out above the aquifer, falls down, and is reabsorbed, so you can get rid of infinite water.
Having a few pumps active around the squares you want to build the walls on will drain the water, this is the
Moses Effect. (And yes, I suppose bilge pumps would work, but it is more dangerous). You have your dwarves build the wall around the stairs, one square at a time, starting with the corners (so they don't get trapped out). The job will sometimes get cancelled, but that just means suspended, so hit
q and hover over the wall and hit
s to unsuspend whenever they do.
You can use just a few dwarves on the pumps, shifting them around to man the pumps most needed after each new segment of wall. When a wall is built, no more water will be able to occupy the square the wall is in.
For an example, I did it in
this thread and posted a picture of the end state.
For any questions on how pumps work, and which direction the dark end should point, see
the wiki. I honestly look at that first colorful picture every time I'm building a pump just to make sure.