Dislodge the broken tile
First of all remove utmost of the grout around the cracked or broken tile by using grout saw. This will decrease the damage of neighborhood tiles.Make few holes with the help of drill machine as it will help to make easy pieces of the tile.
Remove all pieces of the broken tile
By using cold chisel break every cracked or effected tile into many small pieces. Fix the chisel at the midpoint of the damaged tile and hit it smartly by using hammer and keep on hitting until the tile cracks. Try to break it into maximum pieces, the more the pieces will be the more accurately it will break the cracked tile.
Snoop the entire tile piece out from the hole, and clean its whole adhesive residue by using a sharp chisel. Remove all damaged tile pieces and then look at the substrate and make sure that it is undamaged. Test a new tile by putting it down into cleared tile area. Make sure that tile fixes in hole, and that it's blush with the neighboring tiles.
Spread adhesive and replace tile
Take a notched trowel and spread the tile cement on new tile’s back side. Place it on the hole and then press the tile into its place in order to balance its adhesive and base/substrate.
Once adhesive got fixed then use a rubber drift to spread tile grout over all its new and old joints. Clean/ wipe up extra grout by using a squeegee. After that take a tidy towel and wipe it once again to remove any haze.
Strike and seal the grout joints
Take end if a rough toothbrush and strike all the joints near the replaced tile. It would push the grout finely into joints and it will make clean sharp joints. At last use a spray on replaced tile/grout sealer to seal the grout beside dirt and water entry.