The following information is recommended for advanced users only. It is provided as a courtesy, and no warranty or guarantee is expressed or implied for any of the below methods. Results can and will vary; trying anything suggested here or anywhere on the internet is never without risk. The following information is from wikiHow, where other advanced methods are also available.
Take a clean, soft eraser, preferably a new white one acquired just for this purpose. Lightly rub the eraser over the scratch or nick. Continue rubbing until the scratch is gone. Upon completion, follow the directions for cleaning the screen. You may have to rub, clean, and repeat multiple times for the best result.