Scrub the patio with a 2-to-1 mixture of water and degreasing cleanser using a heavy-duty scrub brush. Rinse the patio thoroughly with a garden hose and let it dry for two days. Repair cracks or holes with prepared concrete patch, following the directions for your particular product.
Seal the patio once it has completely dried and any repairs have finished curing. Apply the masonry sealer in straight lines with a low-nap paint roller, working from the interior of the patio to the outside edges. Let the sealer dry 24 to 48 hours.
Lay your tiles out over the surface of the patio. Start in the center and move to each edge, one at a time. Mark the backs of the edge tiles that must be cut to fit with a grease pencil and make these cuts with a wet tile saw.
Remove the tiles from the surface of the patio. Spread the prepared thinset over a 3-foot-by-3-foot area in the center of the patio using a notched trowel. Work the thinset until the surface is level.
Rake the notches on the edge of the trowel lightly over the mortar to give it tooth. Lay the centermost tile in the mortar, pressing gently with your fingertips. Place a 1/8-inch spacer on each side of the tile and lay the rest of the tiles in this 3-foot-by-3-foot space as you did the first.
Tile the rest of the patio, working in one 3-foot-by-3-foot space at a time and moving outward from the center. Remove the tile spacers. Let the thinset mortar dry 24 to 48 hours.
Spread the prepared grout over a 3-foot-by-3-foot square of tile with a grout float. Begin with the interior tiles and work outward, as you did with the sealer. Work the grout into the spaces between the tiles with the tip of the float.
Hold the float so that the edge is angled about 45 degrees. Scrape the edge diagonally across the tiles to remove the excess grout. Wipe the surface of each tile with a damp sponge to remove any grout residue.
Grout the rest of the patio just as you did the first section. Let the grout dry for a full day. Mop the tiles with plain water, if necessary, to remove any remaining grout haze.