Carefully knock out the old tile from the middle to the edges with a hammer and chisel. Then completely remove the adhesive residues and grout. Using an electric scraper is a proven method of doing this. Now the surface is cleaned and new tile adhesive is applied using a small notched trowel.2
Press the new tile into the adhesive bed and line it up. After the specified drying time, grout the joints and leave them to dry. Finally, remove the remaining grout with a damp sponge – done!
The finishing touch: To make replaced joints look "old", simply rub some dirt into the joints until they are roughly the same colour as the neighbouring joints.