Mix the thinset mortar until it resembles the consistency of peanut butter; it should be visibly thick but smooth and easy to manipulate.
Apply the thinset to the center of the tile with a trowel and push toward the corners until the surface is evenly covered with thinset.
Skim the surface of the tile with the trowel to ensure even coverage and remove any excess.
Press the tile to the original tile, following any markings. Ensure that it is properly placed.
Push down on the tile firmly with your hands only, being careful not to hoist your body weight on the tile -- or risk breaking it.
Tap the tile gently into place with a mallet.
Place all the remaining tiles in the same manner.
Allow the thinset mortar the proper time to set and cure by following the directions on the package label.
Apply grout with a rubber-surfaced trowel (if necessary for your tiles) after the tiles have set for at least 24 hours.
Clean out the intersections with the handle of an old toothbrush until smooth.
Wipe off the excess grout with a damp sponge.
Cordon or block off the area from foot traffic until it is safe to walk on and enjoy.