Tape around the old tile with gaffer tape to protect from any tool slipping. Use a mini grinder, cost £15 b&q, or hire for £8 a day hss hire. Carefully cut out the old grout, this takes a few minutes. Is very dusty, ensure room is well vented. Break out the cracked tile and remaining grout. Remove the old thin set with a power hammer, again hire HSS £16 a day. This takes less than ten minutes per tile. Clean area thoroughly with vacuum cleaner. Use a pva sealer to reduce dusty concrete. You then have a sealed level surface to work on. Install the new tile using the appropriate thin set adhesive, buy ready mixed, is dearer but less time consuming, and make sure it is level with the surrounding tiles. Weigh down with a bottle of coke, a large book etc and post a large note to ensure no one steps on the tile. Use folded cardboard in the grout joints to hold tile in place on a temporary basis. When the adhesive is still damp any foot contact will break the seal then the new tile could become loose. After 24 hours grout the new tile.