It took me a while to "get" that diagram too, it is easiest to build from the bottom up.
Start by digging out the bottom level like this
###
#.#
#.###
#..<#
#_###
###
# = Wall
. = Floor
_ = Channel
< = Stairs up
It is best to build a grate over the channel, this will keep surprise beasties from climbing up through there.
Build the pump so that it pulls from the channel (in this case from the south)
###
#.#
#%###
#%.<#
#_###
###
% = pump. The north tile is impassable, and the south one is walkable.
Dig the next level up like this
###
#_###
#...#
#_#X#
#.###
###
X = up/down stairs
You don't need to grate over the channels here (and in fact you can't grate over the southern one).
Once you add the pump (facing the other direction) it will look like this.
###
#_###
#%..#
#%#X#
#.###
###
The south end of the pump is the impassable tile, and it it pulling from the north.
That channel is directly over the output tile of the pump below (the northern most "." in that z-level).
Power passes through the channel under the impassable pump tile in this z-level to the passable tile of the pump in the z-level below.
The next level up looks like the first, but has the "extra" channel for the power to pass through.
###
#.#
#_###
#..X#
#_###
###
Keep building upwards until you get to the top. Then, connect the power source to the top pump.
What the trick boils down to is that the pump must be on two solid tiles (which it is on the bottom level) or have the walkable tile on solid ground with the impassable tile above an existing machine of some kind.
The whole thing can be dug out before adding the pumps, or you can build as you go.