To swap a new tile for a cracked one, start by raking out the surrounding grout with a carbide-tipped scraper. Cover the edges of adjacent tiles with painter's tape to protect them. Then drill evenly spaced holes into the broken tile's pieces with a ¼-inch masonry bit to free them from the substrate. Working from the center out toward the edges, gently tap out the pieces with a hammer and a narrow tile chisel, and clear away any old thinset. Comb an even coating of thinset on the replacement tile's back and on the substrate, and push the tile into place. Let the thinset dry overnight before grouting.