Pull up the old plywood. Use a circular saw to cut through the subfloor along the floor joists and then lift it with a pry bar. Wear work gloves, eye goggles and a dust mask to protect yourself while working with the old material.
Measure the opening and cut sheets of 5/8-inch plywood to replace the old wood. Spread a bead of construction adhesive along the floor joists before dropping the new plywood. Screw the boards into the floor joists.
Lay the cement board over the new plywood flooring, alternating the seams and leaving a 1/4-inch gap around the perimeter. Keep the sheets 1/8-inch apart from each other. Lay the full sheets first and then measure, mark and cut the cement boards to fit. Take the cement boards outside to cut so the dust does not get in the house.
Spread latex fortified mortar over the area under one panel at a time using a 1/4-inch notched trowel. Set the cement board in place and screw in place with cement board screws every 6 to 8 inches around the perimeter along the floor joists. Continue with the remaining panels.
Tape the seams with the same mortar and fiberglass mesh joint tape. Dry the floor overnight before continuing with the new floor covering.