Use warm water to remove dirt and dust from the surface.
Use #800 sandpaper (coarse-grit) and rub in small, circular motions until the scratch is gone.
Follow with #1200 sandpaper (fine-grit) and rub over the surface of the scratch to smooth and blend.
Dry with a towel.
Polish the surface with a cloth and a polishing compound. Any automobile polishing compound will suffice.

Use warm water to remove dirt and dust from the surface.
Using wet #400 sandpaper, gently sand the damaged area in the direction parallel to the scratch. Keep the area being sanded as close to the scratch as possible. Avoid excessive pressure or circular strokes while sanding. Re-wet the sandpaper as needed.
Follow with #600 sandpaper, duplicating the sanding method used in step 2 until the scratch is completely removed.
Dry with a towel.
Apply a small amount of acrylic-based wax (automotive wax) according to the manufacturer's directions. Buff the surface to a shine, using a buffing cloth or drill attachment. Repeat this process as many times as necessary until damaged area is blended with the tub's finish.

What if My Tub Gets Scratched or Stained?