Step-by-Step Guide:

1. Prepare the Area

• Clear the space: Remove any furniture, rugs, or other items from the area around the broken tile.
• Protect surrounding tiles: If you’re worried about damaging other tiles, place painter’s tape along the edges to protect them from accidental scratches or adhesive.
• Wear safety gear: Put on gloves and safety glasses to protect yourself from sharp edges and debris.

2. Remove the Broken Tile

• Loosen the grout: Use a utility knife to cut around the broken tile’s grout lines. This will help prevent damaging the surrounding tiles.
• Chisel out the tile: Place a chisel at the edge of the broken tile and gently tap it with a hammer. Work your way around the tile to lift it out. Be careful not to damage the surrounding tiles. You may need to break the tile into smaller pieces if it’s too difficult to remove in one piece.
• Clean the surface: Once the tile is removed, scrape off any remaining adhesive or mortar from the subfloor using a utility knife or putty knife. The surface should be clean and level for the new tile.

3. Prepare the New Tile

• If the new tile is too large, use a tile cutter or wet saw to trim it to fit the space. Make sure it’s the right size before proceeding.
• Dry fit the new tile to ensure it fits perfectly in the gap.

4. Apply the Tile Adhesive

• Spread the adhesive: Using a notched trowel, spread a thin layer of tile adhesive (thin-set mortar) on the exposed subfloor where the new tile will go. Hold the trowel at a 45-degree angle to create uniform ridges.
• Check coverage: Make sure the adhesive covers the entire area where the tile will sit. Apply more adhesive if necessary.

5. Place the New Tile

• Set the tile: Carefully place the new tile in the adhesive. Press down gently to ensure it makes good contact with the mortar.
• Use spacers: If the surrounding tiles require spacing, place tile spacers around the new tile to ensure consistent gaps for grout.
• Check alignment: Use a level to make sure the tile is even with the surrounding tiles. Adjust if necessary.

6. Allow the Adhesive to Set

• Allow the adhesive to dry and set according to the manufacturer’s instructions, typically 24 hours. Do not walk on the tile during this time.

7. Grout the Tile

• Mix the grout: Follow the manufacturer’s instructions to mix the grout. It should have a consistency similar to peanut butter.
• Apply the grout: Use a grout float to spread grout over the tile and into the gaps between the tiles. Hold the float at a 45-degree angle and work the grout into the spaces.
• Remove excess grout: After filling the spaces, use the edge of the grout float to scrape off excess grout from the surface of the tile.
• Wipe off excess grout: Use a damp sponge to wipe off any remaining grout from the surface of the tile. Be sure not to pull grout out of the joints. Rinse the sponge frequently.

8. Clean and Finish

• Allow the grout to set: Let the grout set for 15-30 minutes, then wipe the tile surface one more time with a clean, damp sponge to remove any haze.
• Let the grout dry: Allow the grout to dry completely (typically 24 hours).
• Seal the grout (optional): If desired, apply a grout sealer to help protect the grout from stains and moisture.

Final Tips:

• If the surrounding tiles are old and brittle, be extra careful during the removal process, as they might crack.
• Make sure the adhesive you’re using is compatible with your tile type (ceramic, porcelain, etc.).
• Always follow the manufacturer’s instructions for adhesive, grout, and sealer products for the best results.