You can remove scratches from the surface of your wooden furniture with a paste made of mineral oil and pumice (available in powder form at hardware stores and paint stores). Use extra fine quality steel wool to rub the mixture into the scratched area. Then clean and polish it with a dry cloth. If you're working with unfinished wood (if you're not sure, it's probably finished), you'll need to be a little more careful not to stain the surrounding wood.
Keep in mind that this side table had a wood finish, so when I tested it, I didn't have to worry about my solutions staining the surrounding wood.