Remove loose tiles by inserting a flat pry bar underneath the tiles and prying them off the backboard. Do not insert from the corners as the tiles may crack.
Scrape edges free of old caulk and any soap scum with a sharp razor knife.
Cut the damaged gypsum wallboard with a drywall saw. Cut in straight horizontal and vertical lines. Use a straight edge to ensure clean cuts.
Scrape off some of the existing grout in adjacent tiles with a grout saw.
Soak the old tiles in a pot of boiling water to loosen the old mastic and drywall paper. Remove from the pot, and scrape off with a putty knife.
Measure the section on the wall that needs to be replaced with new cement backboard. Mark it on the new backboard and cut with a utility knife.
Fix the new cement backboard onto the wall with roofing nails. Hammer the nails into the wall studs. Lift slightly above the bathtub or shower base.
Apply latex mastic evenly over the backboard using an 1/8-inch notch trowel.
Press in the old tiles onto the backboard, making sure to align them with the old tiles.