Measure the floor in front of the fireplace with a measuring tape to determine the size the heart needs to be. Write down the measurements on a piece of paper.
Transfer the measurements for the hearth to a piece of cement backerboard. Score the backer board with a utility knife and snap it to size from the other side.
Glue the backer board to the plywood with construction adhesive. Use a screwdriver and screws to fasten the backer board in place. Use a small amount of mixed thin set mortar to fill the screw holes. Let the thin set dry overnight.
Find the center point of the cement backerboard. Measure the length and width of the backerboard. Locate the center of each direction and snap a chalk line. You should have four quadrants in the fireplace hearth.
Spread thin set mortar on top of the cement backer board with a notched trowel. Lay the tiles in the mortar, starting at the center point and working out toward the edges of the hearth. Press each tile into place and set a tile spacer between the tiles. Use a tile saw to cut the tiles to size as needed. Let the thin set mortar cure overnight.
Use a screwdriver to pop the tile spacers out. Spread grout over the tile joints with a grout float. Remove the extra grout from the top of the tiles with a grout sponge. Allow the tile base to dry for three days before building a fire.
Caulk the perimeter of the hearth. Apply a bead of caulk around the edges where the hearth meets the flooring in the room. Smooth the caulk with your finger and let it dry according to the manufacturer's directions.