Toothpaste Primer
Common toothpaste contains mild abrasives such as fluorite and titanium. Registering "4" and "6" on the Moh's scale, respectively, these substances are of sufficient hardness to polish scratches from acrylic and standard glass watch crystals.
Nothing Fancy
Choose a basic, no-frills white toothpaste. Gel toothpastes have a different formulation and do not offer the same abrasive properties. Specialty toothpastes for bleaching, tartar control or breath-freshening may have reduced abrasive content.
Masking
If the watch is not waterproof and can't be dipped in water after polishing, use masking tape to mask the metal parts of the case and bezel to prevent the toothpaste from getting into crevices.
Rubbing
Place a dab of white toothpaste on a clean rag. Wipe it onto the dry watch crystal. Rub in a circular motion, applying the most pressure to the scratched area. Continue to rub until the toothpaste is a dried haze.
Evaluating Results
Wipe the watch crystal with a clear rag and evaluate the results. Given the mild abrasive properties of toothpaste, it is likely additional applications will be necessary to achieve the best outcome. Approach it as an incremental process of removing the most superficial scratches first, then working down to deeper scratches.
Clean-up
Remove the masking tape, if applied. Use a soft toothbrush and water to remove toothpaste from crevices and metal parts of a waterproof watch.