Load your roughest screening disk (60-grit) onto the screening attachment of your floor buffer. Run the buffer over the entire floor, in rows, taking off the top layer of existing finish. Vacuum up the dust.
Screen with the next-roughest disk (80-grit). Vacuum. Repeat with each of the remaining two screening disks. The floor should be clean, flat and free of finish.
Wipe the whole floor with tack cloths to remove any remaining dust. These are rags dampened with water (if you're working with water-based finish) or paint thinner (oil-based).
Pour down a puddle of polyurethane in the corner of the room farthest from the doorway, making the puddle about as wide as your lamb's wool applicator. Set the applicator in the finish and slowly pull it toward you, going in the direction of the floorboards. Apply the finish in a thin, even layer. Let it dry for 8 hours.
Hand-sand the floor with 220-grit sandpaper, pressing very lightly, to dull the shine of the surface so the next coat of polyurethane will stick. Go over the floor with tack cloths to clean up the dust.
Repeat the finishing and sanding process for the second coat. Apply a third coat, but don't sand it. Let it cure for at least 48 hours before using the floor.