Set a sheet of cement board on the floor in one corner of the room. Trace the edge of the board with a pencil onto the plywood floor.
Pick up the cement board. Spread thin-set mortar over the marked-out space with a notched trowel.
Set the cement board back on the floor, pressing it into the mortar. Step on it to set it firmly.
Drive screws though the surface of the cement board and into the plywood with your screw gun, placing them every 8 or 10 inches over the whole surface of the board.
Lay additional sheets of cement board in the same manner, laying them end to end alongside the wall. Cut the last one with a jigsaw as needed. Cover the rest of the floor, laying the boards in staggered courses so there are no four-way intersections.
Let the mortar set for 24 hours. Press mesh tape over the length of each seam. Spread thin-set mortar over each strip of tape, getting it flat and smooth. Let the mortar set overnight. The floor is now ready for tiling.