Dig out the grout around a damaged tile with a stiff putty knife. With a hammer, tap a cold chisel lightly but sharply on one corner until the tile breaks.
Pry out the broken bits with the chisel. Scrape off old mortar or adhesive with a stiff putty knife; brush the area clean. Spread adhesive on the back of the replacement tile, and set it flush with the surface of the surrounding tiles. Grout and seal the joints.