Rub a piece of steel wool along the grain of the wood over the light scratch. Sand along the scratched wood with a fine-grit sandpaper (120 or higher) for deeper scratches.
Pour a bit of mineral spirits onto a rag and rub the mineral spirits into the scratched area.
Pick up a small bit of wood filler with a plastic putty knife and push it into the scratches on the floor. Wipe it as smooth as possible with the putty knife. Allow it to dry fully. Use a wood filler that is about the same color as the floor.
Sand the wood filler down using 180-grit sandpaper. Sand only the filler.
Apply a polyurethane sealer over the filler to protect it from water.
Set your circular saw to a 3/4-inch depth.
Mark out the boards that need to be removed for the repair.
Start the saw with the front of the saw base plate resting on the floor and the back in the air. Carefully plunge the blade into the wood to cut out the board. Lift the blade up at the end of the cut.
Score the ends of the boards you are removing with a utility knife. Set a chisel into the groove. Hit the chisel with a hammer to break the end of the board clean.
Cut your replacement boards to the correct length and width and place them in the hole. Tap the boards with a rubber mallet. Apply nails to the board. Finish the project by staining the floor with the finish used for the rest of the floor.