Dig out the grout from around the damaged tile with a grout saw, scraping the straight blade forward and back, pulverizing the grout and working down into it. Get as much of it out from around all sides of the tile as you can.
Set the tip of the chisel into the open space along one edge of the tile. Angle the chisel to the line where the tile meets the wall.
Hit the chisel gently with a hammer. Move the chisel a few inches over along the tile and repeat. Keep doing this until you remove the tile.
Use a razor scraper to clean up the exposed wall, getting all mortar and other material off it.
Use a notched trowel to apply tile adhesive to the back of the new tile, covering it completely. Make the adhesive about 1/8 inch thick.
Set the new tile into place, spacing it evenly on all sides. Let it set overnight.
Spread grout over the tile, around each edge, with your rubber grout trowel, pressing it into the space and scraping it off the top. Wipe up the excess grout with a damp sponge.