I still have trouble punching through. I can't quite manage the plug method, and I don't understand the pump method. Unless I get aquifer and volcano, I can't get through without using multiple biomes.
Dude...
Channel a hole into the aquifer. Install a screwpump which will pump from this tile; not after digging a neat little exit corridor with another channeled tile in the end of it, so that you will get rid of the water again. Assign the pumping duty to everyone except your miner, and depending on the nature of your specific case, the engravers OR the masons OR the carpenters.
Get to pumping.
If your aquifer is in rock, send the engraver downstairs to smooth the walls immediately to make the area secure immediately. If you're digging in soil, you need to construct walls though.
Now, make your miner expand the hole in the aquifer by one or two tiles.
Either smooth the walls immediately again; or start the construction of your walls. The cancel-spam is a pain in the arse, but in the end they will manage to build the wall.
Expand some more.
Once you've expanded the room quite a bit, you probably need to place your pump somewhere else so that it can pump more efficiently.
After a while, you will have a neat, safe little room, right there, in the middle of your aquifer.
In the case that you're working with soil and constructed walls, you'll probably have a bunch of tiny little rooms, separated by constructed walls. Demolish these. Build your downward leading ramps or your stairs here and you're fine.
That's really all there is to this.
So. In the case that you have a very deep aquifer, it becomes a bit more complicated, because you need some place to get rid of all the water that you are pumping in every z-level. I guess that two pumps could do the trick, or just having enough room for a little output hole in the ground in each z-level.
One of our posters here had a technique for that, which I haven't had to try yet, because I haven't had to dig through one of these multi level sandstone aquifers yet.