Locate the structure's main water supply shut-off valve at the water meter, then twist the valve in a clockwise direction to turn the water off.
Remove the faucet's handle cover from the center of the handle to reveal the retaining screw. The cover can be removed by prying it away from the handle with a flathead screwdriver or the blade of a dull knife, such as a butter knife.
Remove the handle's screw with a screwdriver, then pull the handle away from the wall.
Remove the escutcheon plate from the bathroom's wall by either removing the plate's screw(s) with a screwdriver or cutting through the caulking that surrounds the lip of the plate with a plastic putty knife.
Grasp the bonnet nut that surrounds the faucet's stem assembly with an adjustable wrench, then turn the nut in a counterclockwise direction to remove it.
Unscrew the faucet's stem assembly with a deep-set socket and a ratchet wrench, then pull the assembly out of the wall. Insert the replacement assembly into the wall and tighten it with the ratchet wrench. Slide the bonnet nut over the faucet's stem and tighten it with the adjustable wrench.
Place the escutcheon plate against the wall and install the plate's screw(s) with a screwdriver. If the plate is held to the wall with caulk, apply a bead of silicone caulking around the seam between the plate and the wall with a caulking gun. Slide the faucet's handle onto the faucet's stem, then insert the handle's retaining screw through the center of the handle and tighten the screw with a screwdriver. Press the handle's cover onto the center of the handle, then turn the water supply on to complete the installation.