Aim the hairdryer at the tile to be removed and warm the tile until it feels softer than the surrounding tiles. Hold the hairdryer 3 to 4 inches away from the tile surface.
Score the tile with a utility knife by making an X across the tile. Stop short of the edges to avoid damaging the surrounding tiles.
Pry the scored edges away from the subflooring, using a putty knife, and gently lift the tile away.
Scrape any remaining adhesive from the sub-floor and replace the removed tile with a new one. Repeat the entire process for each tile, if replacing the entire floor.
Position a grout saw in the center of the grout between the tile to be removed and its neighbors. Avoid contact with surrounding tiles to prevent damaging and then also having to replace those.
Cut all the way through grout to the substrate beneath, making these cuts on each side of the tile.
Break the tile with a hammer, then use the hammer and chisel to lift all pieces still attached to the wall.
Scrape away any remaining setting material or adhesive on the substrate, using a razor scraper.
Wipe the substrate clean with a damp cloth to remove any remaining dust and debris before trying to install the replacement tile.