Turn off the water to the faucet by either closing the shut-off valves in the access panel located on the wall directly behind the shower's faucet, or by closing the main water valve for the house.
Remove the shower handles' screws, which are located either in the middle of the handles under decorative caps or in a small hole near the base of each handle. Pull the handles off the faucet, using a handle puller tool if the handles are stuck and will not come off by hand.
Slide the metal washers off the valve stems and use needle-nose pliers to remove the retaining clips or pins inserted into the valve stems. Clamp a wrench to the base of the valve stems and turn them counterclockwise to unthread the valve stems from the water pipes.
Insert a bath socket over the valve stems if the bases sit inside the shower's surround, and use the bath socket to turn the valve stems counterclockwise. Remove the screws holding the faucet's back plates in place, and use a utility knife to cut away at any caulk on the back edge of the back plates to remove them from the shower's surround.
Install the new shower faucet in the reverse order you removed the old faucet. Turn the water back on and turn on the shower's faucet to check for leaks.