Measure the size of the hearth and transfer the measurements to a sheet of cement backer board. Cut cement backer board to the exact size of the hearth with a circular saw and carbide blade.
Apply a 1/4 inch layer of thin-set mortar on the plywood. Set the cement board into the thin-set 1/8 inch away from the fireplace to allow for caulking.
Drive screws through the cement board into the plywood subfloor to make a more secure base.
Apply a 1/2 inch layer of thin-set mortar over the top of the cement board. Rake the notched side of the trowel through the thin-set to leave ridges on the surface.
Lay the tiles in the thin-set and press into place. Begin at the center point of the fireplace with whole tiles. Place tile spacers between each tile to maintain a uniform distance and to create straight grout lines. Make necessary cuts to the tile with a wet saw. Set cut tiles into the thin-set.
Place a level on each tile. If the tile is not level, adjust it in the appropriate direction until the tile is level. Tap the higher side of the tile with your hand to lower it and make it level or place a piece of wood over the higher side and tap with a mallet until the tile is level. Add thin-set under tile to raise and make it level.
Allow the mortar to set for 24 hours. Remove the tile spacers.
Mix a cement-based grout with water in a bucket to form a mud-like consistency. Dip a putty knife into the grout and load up a rubber grout float. Spread and press the grout into the spaces between the tiles. Wipe up excess grout with a damp sponge.
Apply a bead of fireplace caulk to the space between the tile and fireplace.