Attach a piece of 120-grit sandpaper to a palm or orbital sander, if the scratches are deep or if they cover a large surface. The choice of sander is up to the individual. Orbital sanders have a rapidly rotating head that leaves no swirls behind. They are more forgiving if used across the grain of the wood, and they remove material quickly. Palm sanders move in an up-and-back motion, which requires them to be used with the grain only. Palm sanders remove wood more slowly than orbitals.
Wrap a piece of 120-grit sandpaper around a block of wood for hand sanding smaller areas or for scratches that are noticeable but not too deep.
Sand the scratches with a power sander or with the sanding block. Sand in the direction of the wood grain. Make several passes to level the scratches. Don't be concerned if lighter scratches appear since 120-grit paper, while less aggressive than 80-grit, still leaves behind some scratching. The objective is to slowly smooth the wood.
Change to a lighter, 150-grit paper and repeat the sanding process. Then change to 180-grit to smooth the wood, removing the remainder of the scratches.