(assuming 87-93) You shouldn't have to remove anything depending on the din reducer they used to install the current radio. Usually they have a screw in each corner. Your real task will be wiring hopefully they used an install harness and didn't chop your harness off and hard wire new system. Also depending on the car you have if it has premium sound there is an amp under your pass seat that powers your speaker to get around that when installing an aftermarket you splice around it and cut it out of the system.
Your OEM radio should snap in the housing the two holes on each side are where the removal tool penetrates and by pressing outward you takes pressure off the metal tabs that hold it in. test everything before you snap it in if you dont have this tool. Sometimes you can cut and bend a heavy duty hanger to make these or use 4 small screw drivers