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[Plex]

So I was channelling out a subterranean greenhouse for above-ground crops when I accidentally caved in the above layer of soil, leaving my only miner without any legs and somehow leaving behind a filthy floor covered in shale, unsuitable for crops.

To resolve the issue, I built an aqueduct to add a layer of mud to the greenhouse. It worked nicely, but my crippled miner managed to get himself stuck inside the walled-in greenhouse and began to starve. There was a load of water covering the greenhouse floor, but the poor guy was close to death so I deconstructed the wall. All of the remaining water manages to seep into the main stairwell, down about 15 z-levels until it eventually pooled into the lowest z-level and accumulated into a 7/7 layer of water.

My fortress is young and I need to expand. I'm a little stuck here as I haven't got much experience with fluids.

[Zuglarkun]

Is it just one z-level of 7/7 water? I assume no more water is flooding into the stairwell?

If so, on the z-level above the flooded area, dig out an expanse of space (generally a larger area than the stairwell) next to the flooded stairwell and build a screwpump that draws water from the stairwell. Get a pump operator to pump the water a bit at a time (depending on how much space you cleared) so that the water spreads around the open space and dries up. (1 to 2 deep water dries eventually, 1 deep being faster to dry)

If there is more than one z-level of flooded area, just repeat the steps for each z-level.

If there is still water flooding into the stairwell, you can try a cave in to cut it off at the source, or use magma to obsidianize the source, if you are familiar with how to get magma that is.

[Gwolfski]

make a watersource zone over the water, dig a hole somewhere, put pond (not pit) there, dwarves with buckets and water hauling will take water from stairwell to hole.

[PatrikLundell]

Unless it offends your aesthetic senses, I'd use a rather simple method:
Dig a tunnel sideways from the stairwell, above the water level. Dig a stair down to beside the flooded part (with a single tile wall in between). Dig out an area that's large enough to spread the flooded water so the depth would become less than 2/7 (i.e. a single 7/7 tile would require a total of 4 tiles, including the tile itself and the wall tile). When the area has been dug out, dig through the separating wall, and the water will spread out over the area and eventually evaporate (evaporation takes place when the water depth is 1/7, so if you spread 7/7 over 4 tiles you'll get 2/7 in 3 of them and 1/7 in one. The 1/7 will slosh around, but eventually evaporate, allowing a 2/7 beside it to slosh in generating 2 2/7 and 2 1/7). All this area will be muddied, and thus will be covered by fungal growth when caverns are breached.