Rub a fine steel-wool pad over the damaged areas if the scratches are light. Continue to buff the floor with the steel wool pad until all of the scratches are gone.
Rub nutmeats like almond, walnut or pecan against the light scratches to hide them. A nutmeat with a similar shade can cover those light scratches.
Use a lightweight sandpaper to sand out deeper scratches. Move the sandpaper along the grain of the wood. You can use a small hand sander, but simply holding the sandpaper in your hand and moving it along the polyurethane wood floor can be just as effective.
Rub mineral spirits on the part of the floor you sanded. The mineral spirits pick up fine dust left behind from the sanding and help to smooth out the surface. You can also use a scouring pad soaked in mineral spirits to rub out scratches that are confined to the top part of the polyurethane wood floring. Scour the floor with the mineral spirits-soaked pad, moving in the direction of the wood grain. Dry the floor with a soft cloth.
Use pre-mixed wood filler to fill in the scratches. You can purchase this wood filler at most hardware and home improvement stores. Use a plastic putty knife to apply the wood filler to the scratch, then allow the mixture to dry thoroughly. Sand the spot with a lightweight sandpaper like 180 grit. At this point you should just be sanding away the excess wood filler, not the wood surface itself. Wipe away any excess dust when you are done.
Refinish the previously scrached area with fresh polyurethane to provide a more unified look and feel. Clean the floor regularly to keep it looking like new. Avoid moving heavy furniture across the floor, since that furniture could leave scratches in the wood surface. If you must move furniture, put it on casters or rollers first.