Run a grout removal tool (either a grout saw or rotary tool with grout remover bit) across the grout lines between the tiles. This removes the grout and makes removing the tiles easier. Insert a pry bar under any exposed edge of the tiles and press the pry bar down to lift the tiles from the wallboards underneath.
Sand the remaining grout from the walls with an orbital sander. Remove as much of the remaining grout as possible with the sander. Clean up the residue with a wet/dry vacuum.
Mix shower tile grout in a five-gallon bucket to prepare for the tile installation. Use only grout designed to work with your tile type, as grouts are specifically formulated for ceramic tiles, porcelain tiles and stone tiles.
Scoop the grout onto a trowel and spread it across the installation area. Cover about three square feet of wall space at a time, or just the amount of space you will be able to cover with tile in 10 minutes. Grout dries quickly, so if you spread too much grout, it will dry before you have time to install the tile into it.
Place tiles in the grout and tap them into place with the end of the trowel. Place spacers along the edge of each tile before you lay in the adjacent tiles for a professional installation.
Measure and cut the end tiles for your shower by placing a tile along the edge of the wall. Trace a line on the tile with a pencil. Score the tile surface with a tile cutter. Bend and break the tile by hand. Cut enough tiles to cover the entire wall's edge before you start spreading grout near the end of the wall. That way, you will have to stop and cut tiles in the middle of grouting and setting tile.
Scoop tile grout onto the tile surface when all tiles are installed, spreading it with a float tool. Use enough to cover a substantial area. Work the grout into the seams between the tiles by pulling the grout over the tiles with the edge of the float tool. Scrape off the excess grout and return it to your bucket. Clean the grout residue up with a damp sponge.