Turn the water that runs to the existing fixtures off at the shut-off valve. Turn both the hot and cold handles on to allow the water inside the pipes to drain out the spout.
Place the end of a flathead screwdriver inside the mouth of the faucet and turn it counterclockwise until the faucet stops and you can slide it off. For faucets that slide off, locate the screw underneath the faucet and unscrew it with a screwdriver. Grasp the faucet firmly with your hand and pull it off the pipe.
Pry the middle plastic piece of the handle off with a flathead screwdriver and unscrew the screw securing the handle in place. Some handles have a screw on the side instead of the middle that you must unscrew with a screwdriver in order to remove the handles.
Grasp the handles with your hand and pull the handles off the pipes. Use a plumber’s wrench to pull the handles off if they seem stuck to the pipes. Place the old fixtures in a plastic bag.
Wrap a thin layer of plumber's tape around the threads of the exposed pipe. Slide the new fixtures over the exposed pipes. Use a plumber’s wrench to tighten the fixtures in a clockwise motion until they are flush against the wall and tight. Turn the water supply back on.