Turn off the water supply to the tub. Turn on both the hot and cold fixtures to drain away excess water within the pipes.
Examine the area around the fixture for old caulking. Slice through old caulk around the existing knob with a utility knife.
Slip the edge of your utility knife under the knob cap to pop it off. Unscrew and remove the screw in the center of the knob. Lift the existing knob away from the valve stem.
Clean away mold and mildew on the porcelain surrounding the valve stem with a damp washcloth. Scrape away any dried caulk with a putty knife.
Read the instructions that came with your new bathroom fixture. Attach the new knob. All bathroom knobs are different, but you will likely need to twist the knob itself onto the valve stem and secure it with a knob screw and cap.
Turn the water back on and test the knob to ensure that the fixture works properly.
Recaulk the area around the knob with household silicone caulking.