Maybe I am misreading your question. Are you talking about the liner on the ceiling of the trunk itself (as in directly underneath the rear window), or the liner on the back of the trunk lid (as in the part that swings up when you open it)?
On the trunk lid, there should be plastic screws. On my '95 Coupe, there are 14 of them, and they look like this...
These just unscrew and pop out.
If you're talking about the trunk itself, then the liner is held in on the sides and top by plastic clips, and they look like this...
(Sorry for the blurry picture)
They are very similar to the clips that are used in the door panels. Basically, they're a screw with flanges instead of threads, and you just push them in, rather than twist. Most auto shops (Kragen, Pep Boys, Napa, etc.) sell trim removal tools. The removal tool is just a glorified flat screwdriver with a notch in it, but it's also only a couple of bucks. You can try getting on both sides of the clip with two screwdrivers at the same time, or just buy the tool. You might want to buy a few replacement clips as well, since a few of them always seem to get broken. Either way, just pry away from the body and the clip should just pop right out.