Measure and install a ¾-inch plywood base for the granite tiles. Use the existing countertops as a template for this base. Cut the plywood to size with a table or circular saw. Attach the plywood to the cabinets with a screwdriver and screws. Repeat with a layer of ¼-inch cement backer board. Before screwing the backerboard in place, spread thin set mortar over the plywood with a notched trowel.
Decide on a layout for the granite tiles. The easiest way to do this is to set the tiles on the countertop and move them around until you are happy with the layout. Mark a few layout lines with a pencil and then remove the tiles.
Spread thinset mortar on the cement backerboard. Use a notched trowel to apply the mortar. Press the granite tiles into place and set tile spacers between them. Cut the granite tiles as necessary with a tile saw that has a diamond blade. For the tile pieces on the edge of the countertops, use masking tape to hold them in place while the mortar dries. Install all of the tiles and let them dry overnight.
Remove the tile spacers. Mix the grout per manufacturer directions. Apply grout to the installed granite countertop tiles with a grout float. Use a grout sponge to remove any excess grout from the granite tiles. Let the countertops dry overnight.