Select a location for your porcelain soap dish. Choose a site on the shower wall that is approximately 16 to 20 inches beneath the showerhead. This prevents excessive spray from dissolving the soap and wasting it.
Measure the section of the porcelain soap dish designed to attach to the wall. Mark off a spot of coordinating dimensions on the dry tile wall with a piece of chalk or a sharpened pencil -- this area of tile will be removed completely.
Put on protective goggles. Remove the grout from around the tile in the location where you intend to place the soap dish with an awl or a grout saw.
Punch an "X" pattern into the surface of the tile under the area where the soap dish will fit by using a hammer and nail set to tap the pattern into the face of the tile.
Drill into these divots with a masonry drill to enlarge them and make the holes perforate the tile. Use a 1/4 inch drill bit. Proceed cautiously and drill only through the tile, not the wall behind it.
Pry out the pieces of tile inside the area marked for removal with a hammer and a 1/4 inch cold chisel. Slip the tip of the chisel into a hole and tap its other end lightly with the hammer to crack the tile so it can be pried off the wall. Remove any adhesive and mortar remaining behind the tile as well to create a smooth surface to receive the porcelain soap dish.
Smear tile adhesive onto the exposed wall surface and the back of the porcelain soap dish with a flexible putty knife. Create small ridges in the adhesive with the putty knife to help the dish adhere.
Press the porcelain soap dish firmly into the tile adhesive. Inspect the dish to ensure it is level.
Secure the soap dish to the tile wall with painter's or masking tape to hold it in place while it dries. Allow 24 hours for the adhesive to dry completely.
Add grout around the porcelain soap dish. Use the same color grout that is on the rest of the tiled shower wall. Wait another 24 hours for it to dry before using the shower.