How to tell if there is another aquifer layer below:
As noted, digging an up/down stairs into the aquifer will reveal what is below. A layer which can have an aquifer below an existing aquifer layer, will
always be aquifer,
unless it intercepts the caverns in such a way that it would cause a permanent leak, such tiles have their aquifer quality turned off (but the layer as a whole will still be aquifer).
There are two ways to tell without external knowledge:
1) While the miner is digging, 1-step, once the staircase is dug out, there will be a tick when the bottom of the staircase is dry, if the tile below shows as being wet (dig view) then it is aquifer, otherwise it is not.
2) Before digging, designate another staircase under the first one, then when the first one is dig out if the game immediately pauses to warn about wet stone, it is aquifer, otherwise it is not aquifer (the "is wet stone" check happens the moment the designated tile is revealed, before the staircase above has a chance to accumulate some water).
Digging through aquifers is typically very easy. The twin slit method on the wiki I find complicated to follow and finnicky. When you get to the bottom layer it's so much easier to just seal off a 1x1 or 1x2 staircase and establish a cavern drain if you want to do further aquifer work.
For 1-z level aquifers, unfortunately in this version dwarven mental retardation has reached new heights and I don't know a safe way to use the freezing method - the trick of digging out up/down stairs into the aquifer layer, before channelling them out, will work 95% of the time, but occasionally you get a retard who manages to drown during that step, the rule appears to be "If a dwarf is standing in a tile, and water enters the tile and fills to 7/7, he may drown regardless of how easy the tile is to escape from via ramp or staircase". Short of digging out one tile at a time I don't know a way to stop dwarves going down into the aquifer layer, exposing themselves to either flash freezing or retarded drowning. For the same reason, obsidianization is probably also going to be unsafe due to drowning risk (not that it ever is practical to begin with).
Fortunately, twin slit and cave-in both work as well as ever. For penetrating 1-z aquifers cave-in is
very fast, done right it is totally safe and requires only digging time and 1 construction material (to act as a temporary support) if you're into unsafe you can skip the 1 construction material and channel out the last tile holding up the plug - not recommended although often no-one dies. I don't think the fast-safe-cheap method I use is described on the wiki, it basically exploits the fact that diagonal connections don't provide support, diagonals don't allow cave-in dust to pass through, and dwarves can deconstruct through a diagonal.
While you're digging out the plug, before removing all dirt, build a constructed wall holding up the plug (it must be built over empty space, otherwise it will protect the natural floor from being mined out).
Here is a cross-section of the layer under the surface before collapsing:
#######################
## #<-.dwarf.deconstructs.from.here
# ####O################
# #### #
# #### #
# #### #
## ##
########
# = Dirt
O = Constructed Wall
= Open space
. = Floor
Now once it has been totally dug out and the plug is ready to be dropped, just deconstruct the constructed wall holding the plug up. The dwarf is forced to deconstruct it through a diagonal since there is nowhere else to stand. Because diagonals block cave-in dust, and the dwarf can't pass through, the dwarf is totally safe. Note that if you're not smart about it, dust CAN fly up or down and come in behind the dwarf through non-diagonal connections! or the dwarf can rush up to the surface and eat dust! Using a (locked) door, hatches, or a long enough passageway (about 6 tiles) will prevent this!
The cave-in method basically lets you make any size staircase through a 1-z aquifer you want.
I also sometimes use pumps for a 1-z aquifer if I don't want to vandalize the surface with great pits. Pumps are pretty simple, I normally use a 1x2 slit and use a row of two pumps to keep it dry - you can do it with 1 pump, but 2 pumps are easier. You can also get most the benefits by just moving the one pump (but pumps are dirt cheap).
Finally once you are through it's VERY easy to use drainage from below to make as many holes as you like as large as you like. I've often punched magma pump stacks through aquifer layers this way and also installed skylights into the dining room. It'd be retarded to try and do such things without drainage from below, but with drainage from below you can enjoy 0% suspensions.
The basic method is:
Establish the drain, either into caverns or off map-edge. Don't even bother trying to use atomsmashers or a "large enough room", you want a seriously infinite drain - I've never had a single problem using caverns, though you do take a bigger FPS hit. Note that dwarves can not be flushed through staircases, if they could this method would be ghastly awful, but dwarves are extremely surefooted in staircases with torrents of water gushing down, a dwarf will never under any circumstances by pushed or moved by water down staircases, including through downstairs over open space (i.e. the caverns). Don't ask how this can be, just shamelessly exploit it!
The shaft itself should be dug out using exclusively up/down stairs, every level should be exactly the same. The shaft should extend at least 3 tiles below the aquifer - the bottommost level of the shaft (the level with the drain) will be completely flooded and inaccessible, anything from the 2nd to bottom most level to the level below the aquifer, can be used for safe access.
Once the drainage part is all totally set up, fearlessly punch the shaft of up/down stairs up through the aquifer, even if it's 15 z-levels deep, until you hit dry dirt. Due to bizarro physics this is totally safe, no chance of drowning. Now any rock walls can simply be smoothed. With dirt layers there's a way of doing it with 0% suspensions. Starting from the topmost aquifer layer, channel out all the walls (but not the corners), then build walls in the empty space. Because empty space doesn't accumulate water and because the water can't reach the staircases where the dwarves are standing due to the empty space, there is NO possibility of suspension, 0% chance (except to being frightened by buzzards or w/e). Once the top most layer has been completely walled off, go down to the next level and repeat, until you hit rock. This only works if you go top-down, and avoid channeling out more than 1 z-level at once.
I've routinely used this method to put shafts of about 6x6 through aquifers - much bigger than that and the FPS hit becomes pretty painful, but it still works just as well.
If you want an open-space shaft, then collapse the staircase (i.e. first remove the upstairs at least from the outermost ring, then remove the upstairs from the bottommost layer, finally drop a ring of constructed stairs to "ringbark" the central core, which will then itself collapse from being unsupported). You don't need to collapse the shaft if you want to use it for a pump stack, as up/down stairs function perfectly well as empty space except for the pump inlet tile and the power transmission tile which must be empty space.