Sweep the area around the loose tile thoroughly, and clean around the edges of the loose tile with a damp sponge until all debris and grout dust have been removed. Allow the area to dry thoroughly before continuing.
Measure a carbide-tip drill bit by holding it alongside the grouted area between two tiles. Select a bit that is slightly smaller in diameter than the grouted seam.
Put on a pair of safety glasses, and drill two holes into the grouting -- one hole on each side of the loose tile. The holes should be just deep enough to reach the underside of the loose tile.
Put on a pair of nitrile rubber gloves, and mix equal parts of a two-part epoxy (epoxy resin and hardener) on a piece of cardboard scrap. Use a putty knife to thoroughly mix the epoxy. Load the mixed epoxy into the back of a construction syringe with the putty knife.
Set a golf tee into one of the drilled holes, and firmly place the tip of the construction syringe into the other hole. Fill the hole with epoxy until the golf tee is displaced.
Wipe up any excess epoxy with a sponge, and allow the epoxy to dry for 24 hours. Patch over the epoxy-filled holes with tile grout after the epoxy has dried.