Put the heavy sanding belt in your rented sander. Run the sander over the floor in a diagonal direction to take up most of the existing finish. Don't let the sander stand in one place while it's running, or it will gouge the floor.
Vacuum up the dust.
Re-load the sander with its medium sanding belt. Sand the floor in the opposite diagonal direction as before, taking up the rest of the finish and stripping the wood bare. Vaccuum.
Sand the floor a third time, with the direction of the floorboards, getting them smooth and flat. Vacuum well.
Apply wood stain over the bare floorboards, using a paintbrush. Brush in sections of 4 to 6 square feet, letting the stain soak into each section for about one minute, then wiping up the excess stain with cotton rags. Cover the entire floor.
Let the stain set for 12 to 24 hours.
Brush on polyurethane gloss over the stain in a thin, light layer, brushing with the direction of the boards. Let the gloss set for six hours.
Lightly sand the dried polyurethane with 240-grit sandpaper, by hand, just enough to dull the surface. Vacuum the dust.
Brush on a second coat of polyurethane gloss. Let it set for six hours. Lightly sand it. Brush on a third coat. Let it set for 24 hours.