Buff the scratched area with a polishing compound, if it is not too deep. Buff in a circular motion around the scratch until it is removed, then polish it to bring back the shine.
Wet a piece of 1500 grit sandpaper with water and sand the scratch and surrounding area.
Use a circular motion over the scratch and repeat until the scratch is gone.
Shine the formerly scratched area with a small amount of polish on a clean rag. Repeat this process until the bathtub shines.