First three photos show the before. The last three show the after. This was done on b00gers car.
Tools needed:
1500 or finer sand paper (small sheet is all you need)
plastic polish (should be plastic specific)
cordless drill or a corded drill
blue painters tape for delicate surfaces
cloth buffing wheel (I bought a set from Sears for $15 that came with 3 different sizes)
First rip a small piece of the sand paper. About 1" x 1" is all you need. Wet the sand paper in water or your wash bucket. Using your fingers and light pressure wet sand the "haze" off of the headlight lens. This can take a little while but well worth it.
Don't worry about the foggy (light scratches) look you leave after wet sanding. The idea is to remove the hazy build up as and minimum amount of actual plastic.
Next using the painters tape, tape up the area around the headlight. Extend about 2" beyond the head light lens.
Take the 2" buffing wheel and attach it to the drill. Next take the plastic polish and apply it to the buffing surface of the wheel as well as a light coat on the head light lens. Take the drill and start buffing the head light lens. Start from the top and move horizontally across and down then back up. Stop the wheel and apply more polish if needed, then start from the left side then move up then down across to the right side. Repeat this pattern until you see the light scratches disappear.
With every cycle wipe off the lens with a cloth and inspect the lens. Once polished to your satisfaction move on to the next lens.
Once done with the polishing, if you have a plastic protectant that guards against UV apply it to the lens. (I just used 303).