I was doing some research, but I don't completely understand what happens to the exhaust piping after installing a turbo on your civic? do you remove one side?
or do they meet at some point and continue to the back of the honda?

Erm?

It comes off the turbo and exits like normal.

depeneds on the downpipe some are matched stock or opened later til 2.25",2.5", 3". so you'd have to get a different pipe or exhaust to match it up.

well hopefully your exhaust is going to get bigger when turbocharged. Like mentioned earlier, a downpipe/dumptube can either vent into the atmosphere or be re-directed back into the exhaust pipe, which is quiter. You'll want near 3" exahust turbocharged usually btw.

heres the exhaust route for a turbo'd vehicle.
Turbo/Exhaust manifold (straight off the head)
Turbo
(on some turbo's there is something called an o2 housing between the turbo and downpipe)
Downpipe (from turbo to the cat)
Cat (or high flow cat, or test pipe)
Cat-Back Exhaust
so it's really no different from the Cat on back but from the actual engine to the cat will change.