Work from the center out to remove the broken tile. Drill a hole in the center of the tile using a ceramic tile bit.
Expert Advisor Tip: Put a piece of masking tape in the center so the drill bit doesn't slip.
Before starting, make sure your goggles are on for safety precautions and that the area is clear of water. If you need extra height, use a step ladder or even surface but not the bath.
Drill a small hole in the center of the tile, only driving a little and be careful because the drill-bit may move slightly. Before removing the tile, it may be easier to first rake out the grout from around the edges. Make sure to wear your protective goggles and gloves, use a hammer and chisel to carefully chip out the tile, taking extra care around the sides. Also be aware that some tiles have sharp edges.
Clean off all the old tile adhesive and grout from around the edges and brush away the dust to get a clean surface. Following the instructions on the packaging, apply the correct amount of adhesive on the back of the new tile with a notched spreader. Now fix the tile in place.
Use tile spaces to make sure the tile is in the right position and wipe away excess adhesive with a damp sponge. Read the instructions for information about how long to wait until it's dry and then you can remove the tile spacers. You can use ready mixed grout which should be applied generously with a grout spreader. Make sure to ease it into each of the joins around the tile. Wipe away excess grout with a soft rubber spreader.
Create a smooth finish with your finger around the tile. If the tile has sharp edges, its best to use a grout finisher instead so you dont cut yourself. Finally, get rid of any excess grout before it sets using a damp cloth or sponge.
If the new grout stands out against the old tiles, you can simply rake out some of the grout that's surrounding the new tile and re-grout the whole thing so that it blends in. Alternatively, you can use a grout pen which is quick and easy way to enliven discolored grout.
Don't forget to save your leftover tiles. It can be a little tricky later on matching the old tiles to the new ones. All supplies needed for this project can be found at your local Friedman's Home Improvement.