Close the doors to the room and tape plastic tarps over them so the dust doesn't drift out through the sides of the door. Close the vents in the room. Go over the floor with a hammer and center punch to knock down any raised nail heads. Load the rotating floor buffer with an 80-grit flooring screen. Turn it on and move it immediately across the floor, going with the direction of the floorboards. Move it forward and back, removing the top layer of gloss. Make sure the scratches from the chair legs are removed completely.
Vacuum up the dust. Make sure you cover the entire floor, and use an edge tool to get into the corners.
Put a 120-grit flooring screen on the buffer. Screen the floor a second time, smoothing out the deglossed surface. Vacuum.
Brush on a coat of polyurethane with a paintbrush, starting at the farthest part of the room from the doorway so you can work your way out. Brush on the polyurethane in thin, even strokes, going in the direction of the floorboards.
Let the polyurethane dry for six to eight hours. Sand it with 300-grit sandpaper by hand, very lightly, so it just dulls the shine. Vacuum.
Brush on a second layer of polyurethane in the same manner as the first. Let it dry. Sand it. Vacuum. Apply a third polyurethane layer. Let it dry for 24 hours.