I'm a little late to this thread, but had the same issues building an above ground bog a couple of years ago. I built a wooden frame, lined it with EPDM, installed the piping as Addy1 described, (the only difference was I laid my pipe on bricks that were laid on the bottom a few feet apart with two layers of liner under them.
Beginning construction
Adding the walls
Adding piping
Checking for leaks
Time out for a little playing
Filled with pea gravel and nearly finished top edge.
The pond water is pumped into one end of the bog, perculates through the gravel then surfaces to flow to the other end. It's a little hard to tell, but the end is about 4" lower than the main body of the bog. When the water reaches that level it spills into a catch box then spills into the sluice which in turn runs under the "dock" boards and back into the pond.