Wipe away the scratched area with a rag or damp cloth – this will remove any excess debris from the scratch and prep the area for a filler.
Use a lightweight sandpaper to work out the scratch. You may have to sand the surrounding areas so the result is a smooth finish. Be careful not to sand away any deeper than the scratch or you will make a noticeable hole in your floor.
Apply mineral spirits to a small, dry cloth until half of the cloth is saturated but not dripping. Rub the cloth and the spirits into the deep scratch. Work the cloth into the scratch in order to remove all excess dirt and debris.
Stir the wood filler putty can with your plastic putty knife so that the mixture is thick and free of liquid or excess oil. Use your plastic putty knife to work a small amount of filler into the scratch area on the floor. Continue to work the putty into the scratch until it is even with the floor's surface and there is no sign of the scratch. Allow to dry overnight.
Sand the scratched area with a lightweight sandpaper. Work the paper back and forth carefully to avoid further scratching, but just enough to smooth out the putty and the surrounding wood planks. Use a paintbrush or small lamb's wool roller to apply wood stain or a polyurethane finish to the where the scratch once was. Blend in the stain with the surrounding wood using one to two light coats until complete. Allow the wood to dry completely or at least 48 hours before walking on it.