If you need to replace a cracked ceramic tile and have or can buy one that matches, the procedure is as follows.
Use a grout saw to remove the grout around all four sides of the damaged tile.
If the edge of the tile is loose you may be able to pry it up by using a pry bar or screwdriver and protecting the adjacent tile with cardboard. (a pry bar is better because it will distribute the force over a wider area and make it less likely you will crack another tile.)
Clean the surface under the old tile, coat the back of the new tile with adhesive and set it into place.
Lay an 18″ section of 2 x 4 over the new tile and gently hammer it down until the new tile is level with the old. Let the adhesive dry and then grout and seal the gaps.