Unscrew the kick plate (the bottom metal skirt) by using a screwdriver. Place the plate to the side.
Take out the compactor drawer. Depending on the make and model of the compactor, removing the door will be as simple as sliding it out, or you may be required to remove screws near the drawer tracks.
Pry the garbage compactor trim from the edge of the counter using a crowbar or putty knife.
Slide the old compactor out of the cubbyhole. You will likely have to lift it up an inch or so before sliding it out.