Turn off the water supply.
Disconnect the drain by removing the drain basket with a screwdriver. Remove the overflow valve, as well.
Remove the locknuts that connect the tub to the drainpipes underneath. You may have to go through the wall on the outside or through the ceiling underneath your bathtub. Use a wrench to loosen the locknuts that connect the tub to the pipes.
Remove the fixtures in the tub and shower unit, using a screwdriver to take out the screws that secure each piece to the unit. Slide the faucet handles, shower head and tub faucet out. You may need a wrench to remove each piece from the water pipe. The spout will need to be turned counterclockwise in order to remove it.
Push a rag or piece of newspaper into the water pipes to prevent debris from going into them.
Cut the caulk from around the tub and shower surround where they are attached to the wall, using a putty or utility knife.
Place the flat edge of a pry bar or the claw of a hammer into the gap between the shower surround and the wall and pull back firmly, but gently, on it.
Continue prying in this manner around the tub and shower until the glue is released.
Grasp the surround and pull it out and away from the wall. If you have trouble prying it, consider using a reciprocating saw to cut the surround into pieces. Be careful, when using a saw, that you don't cut into studs behind the shower. You may not, in this case, be able to save any drywall that's behind the shower and tub.