Warning: This is for PLASTIC headlights/foglights. Do not attempt on glass.
What you need:
Sandpaper - 400, 800, 1000, 1500, and 2000grit (total of $8 at hardware store)
ScratchX or PlastX ($5 at autozone, advance auto, pep boys, etc)
Soft cotton cloth, or microfiber polishing/waxing pad
Total Cost = $13......compared to hundreds of dollars for new headlights and foglights
Step 1: Wet Sanding
2) Get a bowl of water and dissolved a few drops of dish detergent
3) Wet sandpaper and sand with light to moderate pressure in horizontal direction.
4) Rinse, repeat in vertical direction
5) Rinse, repeat in small circles
7) Repeat steps 1-6 with 800grit sandpaper, then 1000, then 1500, and finally with 2000grit
Here a some pics of the process to give you an idea of what things will look like after some of the sanding stages (forgot to take a pic of 1000grit, but you catch my drift)....
Step 2: PlastX Application
1) Everything needs to be completely dry. So wipe with some paper towels and let air-dry for a few minutes.
2) Apply a few drops of PlastX to the lights
3) Use cloth or microfiber pad and rub in small circles until the PlastX begins to disappear
(You are filling in the fine scratches left from the 2000grit sandpaper to give it a smooth finish.....don't rush this step, it may take a good 3-4min depending on the size of the lights)
4) Once the PlastX is nearly gone, use a clean part of the cloth and wipe of the excess thoroughly. (You will hear a high pitched squeaking sound when all the residue has been removed.)
5) Stand back and admire your work!!!
Step 3: Prevent Future Damage
I added 3 coats of car wax to each light to protect them from hazing/oxidation...2years later they are still looking great.
Also, you can try spraying one or two coats of clear acrylic spray for maximum protection