Install a replacement soap dish of either the retrofit style or in plain tile.
Replace soap dish tile wall.
Place masking tape over the tile.
Regrout after 24 hours.
Loosen the old grout if the soap dish has fallen entirely off the wall you can skip ahead to the third step.
The tape will help keep the drill bit from slipping and ruining an adjacent tile when.
Clean the area the new tile will not.
Install a 1 4 inch masonry bit.
Shower soap dish holders do not last long.
Using a hammer and nail punch small divets into the tile in an x pattern.
With a section of fine grit sandpaper in the 180 to 100 range roughen up the back of the soap dish and the ceramic tile wall.
To help it shatter drill.
Use thin set and hold your new soap dish in place using long strips of duct tape crossing the new dish tile.