Whether you use Brasso, toothpaste, or one of the commercial
plastic polishes to clear up the haze, the technique is largely the same.
Just put some on a small cloth and use it as if you were using a very fine rubbing compound, turning the cloth as needed and re-wetting with the polish, then finishing with a clean, dry cloth. Repeat until any haze, scratches, and pitting disappear. These products generally are very fine abrasives, not just cleaners, so they actually grind out the scratches and pits, with a little bit of effort.
After polishing plastic parts
, often the plastics haze over much quicker than they did originally. This is because the manufacturer coats the lens with a protective layer, which polishing removes.
Some of the polishing kits have a final protective coating you put on, after polishing. You can also use a product like 303 Aerospace Protectant or paste wax. These after-treatments may help the repair last longer.