As we have already indicated on this webpage, regarding tile, it is a brittle material and easily cracked. Based on this characteristic, a tile is easily cracked and broken by striking the center of the tile with a standard hammer. You can position a screwdriver in the center of the tile and sharply strike the handle of the screwdriver. In most cases this will cause the tile to break, and will allow you to pry pieces of the broken tile off the backer board. Carefully remove only the tile that is damaged or you have identified as requiring removal. Clean the entire area where the tile was, and make sure to remove all the old mastic that had adhered the tile to the substrate.
Once the tile is adequately removed and the area cleaned, an adhesive is required to install the new tile in the place of the old tile. Many installers will simply use the same mastic that was used when the entire field of tile was installed. This type of mastic will provide the adhesion required to install the new tile, however, I prefer the specific products that have been developed for this application. Manufacturers have added admixtures to their common mastic, to enhance the bonding and the adhesion. These admixtures will perform better than the standard mastic, if the substrate has not been adequately cleaned or there is any other compromising issue.
The most difficult step in the installation of a replacement tile is the matching of the grout around the tile. Unfortunately, what normally occurs with grout is that it changes color and shading due to repeated cleanings, sunlight or water. This makes any new grouting in the field alongside the old grout, to stand out. There are techniques to color the new grout to make it look like the old grout, however, this matching is usually performed by a professional tile contractor and takes experience and patience.