Lens scratches are the bane of any photographer's existence--a scratch on the surface of the lens can ruin any picture. If you do happen to get a minor lens scratch, however, there is a simple way to polish it out.
Remove the scratched lens from the camera body (if it is on a SLR body), or extend the lens as far as possible from the body.
Use the lens brush and blower to clear any large debris that may be on the lens surface. Apply a drop of lens-cleaning solution to the lens-cleaning cloth and clean the lens of any additional dust and debris that may cause further damage to the lens.
Find the location of the scratch by angling the lens and looking at the surface for scratch lines.
Apply a very small amount of toothpaste or polishing compound to the lens on top of the scratch. Using too much paste or compound could ruin both the lens mount and the protective coating on the surface of the lens.
Using a corner of the lens cleaning cloth, very gently rub the toothpaste or polishing compound into the surface of the lens, over the scratch. Wipe excess compound or paste away, then buff the lens until the scratch can no longer be seen.
Install a UV filter on the outside of your lens to prevent foreign objects from scratching the lens.
Glass camera lenses have a protective coating on the outside of the lens. Buffing or polishing with any sort of abrasive could remove this coating and destroy your lens. Take extra precaution when using this method.