The first step in installing a new bathtub surround is to remove the fixtures, including the faucet, shower head and tub spout. Make sure the water is turned off before removing the screws that hold the fixtures in place. If you cannot find any screws on your spout, you can unscrew it with a pipe wrench or insert a pair of pliers into the spout and turn.
Once the fixtures are removed, tear out the existing surround and remove any backerboard. If needed, cut out drywall above the old surround to make room for the new surround. Be sure to wear safety glasses for this step, and mask off your tub with cardboard to protect its finish.
When installing the new surround, begin with the long, back panel. Set it on the tub rim and temporarily nail it into place. Place the side panels on the walls next. Remove the side panel that contains the faucet and fixtures, and measure the necessary spots for the connections. Use a hole saw mounted on a drill to make a clean cut. Place the panels back on the wall, and secure them in place with the fasteners recommended by the surround manufacturer.
After the surround is in place, you can reconnect the plumbing. Run a bead of silicone along the edge of each opening that you've cut for each fixture. Reinstall the faucet plate, tub spout and shower head. Run the water in the tub to make sure that there are no leaks.
Use latex or silicone caulk to fill in any spaces between the walls and the surround. Work in small sections, and use the least amount of caulk possible. Use your finger to quickly spread it before it hardens.