By Gene and
Step 1 : Dislodge the broken tile
Remove as much grout around the broken tile as possible with a grout saw. This will help prevent damage to the surrounding tiles.
Step 2 : Remove all pieces of the broken tile
Use a cold chisel (a thick short steel bar with a flat-tapered point) to break each damaged tile into several pieces. Wear protective eyewear when breaking the tiles.
Set the chisel at the center of the tile, and strike it sharply with a hammer until the tile cracks. Proceed to break the damaged tile until each tile is broken into six or more pieces.
Pry all the tile pieces out of the hole, and then use a sharp chisel to clean away any tile remnants or adhesive residue. Remove all the damaged tiles, and then inspect the base or substrate to be sure that it is intact. Test-fit a new tile in the area. Be sure that the tile fits into the hole, and that it's flush with the adjoining tiles.
Step 3 : Spread adhesive and replace tile
Use a notched trowel to spread tile adhesive on the back of the replacement tile. Press the tile into the hole, and twist it to ensure full contact between the tile adhesive and the base or substrate.
Step 4 : Apply grout
When the adhesive has set, use a rubber float to spread tile grout over the joints between the old and new tiles. Wipe away excess grout with a squeegee and then use a clean towel to wipe away the remaining haze.
Step 5 : Strike and seal the grout joints
Use the end of a toothbrush to strike the joints around the new tile. This pushes the grout deep into the joint and results in clean sharp joints. Use a spray-on clear tile/grout sealer to seal the grout against grime and water entry.