Heat a clothes iron and place it on the loose tile. This will release the adhesive from the tile.
Lift the loosened tile with a putty knife by placing the putty knife under one edge of the tile and wiggling the knife until it removes the entire tile. Never scrape under the tile or try to force the tile to move because the tile will break.
Scrape the floor area where the tile had been with the putty knife to remove dried adhesive.
Pour a capful of mineral spirits on a rag, and wipe the area on the floor to dissolve any leftover adhesive. Be careful to rub only in the open spot so you do not remove adhesive on other tiles.
Spread new adhesive onto the spot with the putty knife. Wait until the mineral spirits have dried to prevent the spirits from dissolving the new adhesive.
Replace the tile in its spot and roll over it with a rolling pin to even the tile with the other tiles.
Place grout into the spaces around the tile using the putty knife and smooth the grout with your finger covered by a rag.
Wipe down the surface of the tile with a clean rag to remove any adhesive or grout that may have been smeared.