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.
Shower soap dish holders do not last long.
Remove the broken soap dish a fractured soap dish may almost fall off the wall by itself.
The soap dish tile remove the grout around the tile with a grout saw.
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.
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.
To help it shatter drill.
Install a replacement soap dish of either the retrofit style or in plain tile.
Install a 1 4 inch masonry bit.
Clean the area the new tile will not.