Remove the existing shower walls. Cut the walls in half with a reciprocating saw and remove the walls by prying them away with a crowbar. Pry off the drywall under the shower walls with a hammer and crowbar as well.
Remove the mounting screws along the lip of the shower base with a screwdriver and unscrew the shower base drain with a drain wrench. Remove the base by sliding it out of the showering area. Clean the showering area with a brush and dust pan, removing all debris.
Level the floor with a carpenter's level. Mount a shim to the floor with a 1-inch screw in areas where the floor drops below level. Fit the showering base into the showering area. Mark the location of the shower drain with a pencil on the floor under the base. Remove the base and cut a hole in the floor with a jig saw or hole saw at the mark. If the drain hole lines up with the shower base drain, skip this step.
Install the drain into the shower base by placing the top half into the base drain hole. Place the gasket around the bottom of the drain and connect the bottom half. Tighten the bottom half to secure the drain in the shower base.
Slide the shower base back into place. Level each side with the carpenter's level. Slide shims under the base in areas where it falls below level. Mount the base to the framing of the surrounding walls with 2-inch screws and a screwdriver.
Replace the cement board. Cut cement board to fit on the walls with a cement board saw. Mount it to the framing with drywall screws and screwdriver.
Install the shower walls. Place the walls on the cement board with the bottom flush to the shower base to ensure a proper fit. Apply adhesive to the cement board with a plastic scraper or applicator and press the walls in place. Allow the adhesive to dry for up to 24 hours or as indicated on your shower wall installation instructions.