Clean the hardwood floor thoroughly with floor cleanser, using a scrub brush. Rinse the cleanser with a mop. Let it dry for 48 hours.
Lay a piece of Hardiboard on the floor, in one corner. Trace around the perimeter of it with a pencil. Pick up the board.
Spread thinset onto the marked area with notched trowel, coating it all in roughly ¼-inch layer.
Drive 1 1/4 galvanized drywall screws through the Hardiboard, straight down, in a grid pattern every six inches, using your screw gun.
Lay the next sheet of Hardiboard off the end of the first, securing it in the same way, with mortar and screws. Repeat, laying the sheets off each other end to end. Cut the last piece to fit, scoring it with a utility knife and breaking it in two to fit.
Lay the next course of Hardiboards starting from the opposite end where you started the first course, so the ends of the boards are staggered and there are no four-way intersections. Cut the final board as needed.
Repeat, covering the whole floor.
Lay drywall tape over the seams of the boards, pressing it firmly over each line. Spread thinset over each strip of tape, just enough to cover it. Flatten the mortar completely.
Let the mortar dry for 24 hours. Tile the floor.