Place the edge of a chisel along the grout line of the damaged tile section. Strike the end of the chisel with a hammer to break away the damaged tile and backer board. Continue this process until you have removed the entire damaged section.
Unscrew the backer board screws with an electric screwdriver. If the backer board was nailed to the studs, remove the nails with the claw end of a hammer.
Measure the exposed section of the shower wall with a tape measure. Transfer the measurements to a new section of cement backer board. Score the board along the measurements with a utility knife, and snap the board along the scored lines.
Put the cement backer board in place. Drive 3-inch screws through the backer board into the wall studs at 4-inch intervals with an electric screwdriver.
Apply thinset mortar to the backs of ceramic or stone tiles that match your existing tiles. Press the tiles into place on the backer board.
Fill the spaces between the tiles with grout using a grout float. Work in small sections, wiping away excess grout with a damp sponge as it begins to dry.