Attach a piece of 60-grit sandpaper onto a belt sander and plug the cord into an electrical outlet. Don safety glasses and a dust mask for protection. Sand the areas of the floor where the splinters and cracks are visible until you can no longer feel any rough patches.
Wipe the floor off using a tack cloth to remove the excess dust from the surface.
Open a tub of wood filler and scoop out 1 or 2 teaspoons using a plastic putty knife. Spread the putty over all imperfections in the wood floor, including any cracks, depressions or other gouges. Scrape off as much of the excess putty as possible and allow the putty to dry completely.
Sand the wooden boards using a 100-grit sandpaper until the wood putty is the same level as the floor boards. Wipe the boards again using a tack cloth to remove the dust.
Open a can of wood stain in the same color as the original floor and apply it only to the repaired boards using a foam paint brush. Drag the foam brush over the can rim so you don’t drip excess stain on other boards.