Remove damaged tiles by prying them loose with a flat chisel.
Cut the broken edges of the old drywall with a drywall saw to create neat and straight seams.
Scrape off any residual caulking from the shower base or bathtub base with a sharp razor knife.
Scrape off old grout with a grout saw from surrounding tiles around the immediate damaged tiles. Remove a thin layer of grout.
Soak the old tiles in boiling water and scrape off old mastic with a wide putty knife from the back of the tiles. Do this only if the tiles are salvageable. If the tiles are broken, replace them entirely.
Measure the section needed for the new baseboard and mark it on a new piece of cement backer board. Slice through the fiberglass mesh and score the marked line with a utility knife. Score the baseboard until it can be snapped off. Fit the backer board into the wall to make sure that it fits, with the smooth side facing outward.
Attach the new backer board by hammering roofing nails into the wall studs. Keep the backer board a little above the shower or bathtub's base, leaving about 1/8-inch space between the base and the bottom of the backer board.
Apply latex mastic on the backer board with a 1/8-inch notched trowel. Spread evenly on the surface.
Press the new or salvaged tiles on the backer board, aligning joint lines to maintain uniform joints. Let the mastic dry for three days.
Mix powdered grout with a latex additive following the manufacturer's directions. Apply the grout mixture into the joint lines with a rubber trowel. Wipe off excess grout with a damp sponge and let the grout dry for two to three hours. Then buff the tiles with a soft cloth.
Fill in the gap in between the shower base and wall with silicone caulk. Fit the caulking tube in a caulking gun and squeeze a small amount into the gap. Smooth out excess with a gloved finger.
Finish by sealing the grout joints with liquid silicone sealer.