Remove the old grout from the sides of the damaged tiles using a hammer and small tile chisel. Break through the grout applying firm pressure. Avoid contact with the surrounding tiles to prevent damage to them.
Hit the damaged tile firmly with a hammer to crack it through to the substrate. Pry up and remove all pieces of the broken tiles using a chisel.
Remove the remaining grout completely by gently tapping it with your hammer and a small chisel.Scrape old thinset (bonding) material from your substrate with a wide blade chisel or paint scraper.
Apply a thin layer of thinset to substrate using a notched trowel. Spread thinset onto the back of the new tiles.
Set the tiles into position. Press the tiles down firmly centering them in the spaces. Allow the thinset to dry for at least two hours before proceeding.
Mix grout according to the package instructions.
Dampen grout in the surrounding tiles to prevent the old grout from absorbing the moisture from the new grout material.
Spread grout into the spaces between tiles using a rubber grout float. Smooth it with your fingertips.
Let the grout dry for at least 15 minutes, until it no longer feels tacky. Wipe away excess grout with a damp sponge. Wait 24 hours before walking on the new tile.