Trace the size of the vanity top onto a piece of 3/4-inch plywood and cut out the plywood on a jigsaw. Place your sink and faucet hole templates in the position they will be on the vanity and trace around them on the plywood as well. Cut out these holes with the jigsaw.
Place the plywood vanity top onto a sheet of concrete backerboard and trace all around it, as well as the sink and faucet holes, onto the backerboard. For straight lines, score the backerboard with a utility knife and snap along the score lines to cut it. Use a nail hole punch to outline the curved lines then gently push out the backerboard from within the cut lines.
Sit the plywood in place on top of the vanity. Drill pilot holes sized for the shaft of 1 1/4-inch screws every 5 to 6 inches around the plywood into the vanity underneath. Secure the plywood in place with the 1 1/4-inch screws, ensuring the heads of the screws are level and not protruding above the plywood.
Spread a 1/8-inch-thick layer of thinset mortar over the plywood and use the notched side of the trowel to create furrows in the surface of the mortar.
Place the backerboard on top, ensuring the sink and faucet holes in the plywood and backerboard match up. Press down firmly to bond the backerboard with the mortar. Secure the backerboard in place with roofing nails driven every 6 to 8 inches on center through the backerboard into the plywood underneath.
Rough in the tile design on the backerboard using a chalk line. The easiest way is to make a grid whereby one square of the grid equals one tile. Don’t forget to factor in the edging tile in the grid.
Spread a 1/8-inch-thick layer of thinset mortar over about four or five squares of the chalk grid and furrow the mortar. Set the tiles in place on the backerboard using tile spacers to create a uniform gap between each tile. Continue laying tiles this way until the only tiles left are the edging tiles, and those needing resizing to fit.
Cut the tiles needing resizing with tile nippers and spread mortar on the backs of these tiles before placing them individually in position. Spread mortar on the backs of the edging tiles and place them in position along the edge of the vanity top. Leave the tiles overnight for the mortar to set.
Remove the tile spacers and spread grout into the joints between the tiles using a grout float. Don’t apply grout to the joints around the sink and faucet holes. Let set for 30 minutes, then wipe over the surface of the tiles with a clean rag to remove the excess grout. Apply caulk to the joints you left without grout around the sink and faucet holes. Use a wet finger to smooth over the caulk. Let the grout cure overnight.
Apply three coats of tile sealer to the vanity top, waiting the appropriate drying times between coats as specified by the sealer manufacturer.