Purchase a touch-up marker from a home improvement store. Choose one that closely matches the color of the finished wood.
Rub the tip of the marker into the scratched areas. Only use the marker in the scratches. If you accidentally get some outside of the scratches, wipe it off immediately with your rag.
Apply a small amount of paste wax to your rag. Apply the wax to the entire area around the scratches you repaired.
Wait for the wax to haze over, then buff it out using your rag until the surface is glossy. If the waxed area has a noticeably different shine than the rest of the wood, apply the wax to the entire wood surface.
Rub sandpaper around the scratch to ensure that the area around the scratch is level.
Dampen a rag with mineral spirits, and wipe down the area.
Find a wax stick that matches the color of the finished wood. You can combine pieces of multiple wax sticks in your hand to blend their color.
Rub the wax over the scratch until it is completely filled.
Slide your straight edge over the waxed area, picking up and removing any excess wax. Once the wax dries, you can coat the wood with any finish that you like or just leave the wax as it is.