Close all doors and vents in the room.
Load the rented drum sander with its 60-grit sanding belt. Start the sander and immediately begin moving it over the floor in a forward-and-back motion, with the direction of the floorboards.
Gradually work your way across the floor, continuing to sand forward and back, with the direction of the boards. The sander should take up the gloss layer and much of the underlying stain, digging into the wood. Do the whole floor. (Note: Never let a drum sander remain in one position while it's moving or it will dig too deeply into the wood and damage the floor.)
Thoroughly vacuum the floor, taking up all the dust.
Reload your sander with its 80-grit belt. Repeat the sanding process, taking up the remaining stain so the unstained wood is completely exposed. Vacuum the dust. Sand a third time, with the 120-grit belt, to smooth out the surface. Vacuum thoroughly.
Apply light wood stain over the floor with a brush, starting in the corner of the room furthest from the doorway. Brush it heavily over a few square feet, let it sit for one minute, then wipe up the surface material with paper towels, leaving the wood lightly stained. Repeat, working across the whole floor a few square feet at a time.
Let the stain set overnight. Coat the floor in polyurethane, brushing it with a paint brush in a light, thin coat, with the direction of the floor boards. Cover the whole floor.
Let the polyurethane set eight hours. Dull the surface by lightly hand-sanding it with 220-grit sandpaper. Vacuum the dust.
Brush on a second polyurethane layer. Let it dry eight hours. Dull it as before. Vacuum the dust. Brush on a polyurethane third. Let it set 24 hours.