@Notere It's hard to understand what you were doing. Without understanding the mechanics of water dynamics in DF, it's pretty hard to find a solution. I'll try to explain by pointing out some bits that look like they may have tripped you up. When you start, here is what the last non-aquifer layer should look like:
Here's what the first aquifer layer should look like
You build floors over the lower 2 stair tiles in the non-aquifer layer so you can pump from left to right. But you have to remove the down ramp in the lower left tile (only!) by channeling down. This is because you can't use the pump over the down ramp. Don't channel out the upper left one because otherwise your dwarf won't be able to get back out. Note: you are only using 1 pump -- from the lower left to the lower right!
Once most of the water is gone, send a dwarf down to create up/down stairs in the two *aquifer* layer tiles on the *left hand side only* (Note that in the picture they use a slightly different hashing for the non-aquifer layer and the first aquifer layer).
When you are done, your aquifer layer will look like this:
Err... well, pretend that you mined those out... Important: When mining out the first one of these stair cases, step using the "." until the layer *below* is revealed. Then use "k" to check to see if the layer is damp or not. If it is not damp, then there is no aquifer below that level and you have to skip down to the last section. If it *is* damp, then you have at least 2 aquifer layers and you can drain into the bottom one.
Once you've mined out those two stairs, disassemble the pump and reassemble it the other way around -- on the bottom only! Again, we are using only 1 pump! Do not put it on the top! Follow the exact same instructions as before, replacing "left" with "right". Keep in mind that we are working only on the *bottom* right here. Do *not* mine out the down ramp in the upper right corner!
At this point you can dismantle the pump. You do not need it because the aquifer is draining into the level below.
Your non-aquifer layer should look like this (well, instead of a pump there, you'll have floors -- you can disassemble the floors now too and be left with your original staircases):
First aquifer layer should look like this:
The aquifer layer below that should look like this:
In other words, you have *2 aquifer layers* which have up/down stair in them and you are going to work on the first of those.
Next dig out sections *in the first aquifer layer* and add walls until you get this:
I recommend doing it one at a time (dig a space, add the wall), even though the wiki says to do it 4 at a time. Just until you get used to the process. It doesn't matter what order you do it in.
Next dig an up/down staircase in the centre and then an empty space above/below it and add a wall:
Do top/right, bottom/right, bottom/left, top/left (I don't think the order matters) until you get:
Remember, there is no pumping involved! It is just draining into the aquifer below.
After that is done, you are essentially back to the starting place. Your first aquifer layer is the same as what you had in your last non-aquifer layer when you started except the downramps are up/down staircases (it really doesn't matter). You can go down as many layers as you want until you get to the bottom.
It gets tricky once you get to the point where there is one more aquifer layer to wall up, but there is no aquifer layer below it. Then you *must* follow the instructions in the wiki *exactly* from
http://dwarffortresswiki.org/index.php/DF2014:Double-slit_method#Walling_off_the_last_aquifer_level.
Hope that was helpful. I know I'm just restating the wiki, but I hope that stressing different things will get you into an "Aha!" moment. The aquifer layers before the last one are really very easy. The last one is very tricky.