Use thin set and hold your new soap dish in place using long strips of duct tape crossing the new dish tile.
Replace soap dish tile wall.
Using a hammer and nail punch small divets into the tile in an x pattern.
Install a replacement soap dish of either the retrofit style or in plain tile.
Loosen the old grout if the soap dish has fallen entirely off the wall you can skip ahead to the third step.
Place masking tape over the tile.
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.
The tape will help keep the drill bit from slipping and ruining an adjacent tile when.
The soap dish tile remove the grout around the tile with a grout saw.
Regrout after 24 hours.
Be careful when sanding the tile wall so that you are not extending your scratches beyond the soap dish s future footprint.
Clean the area the new tile will not.
To help it shatter drill.