See short 2:23 video and steps below.
Step 1: Hazy Headlights - Wash First
Step 2: Materials: Meguiar's Cleaner Wax (Walmart), 2000 Grit Sandpaper, Microfiber Cloth, Water Bowl
Step 3: Tear Off a Piece of the 2000 Grit Sandpaper
Step 4: Wet Sand the Headlight to Remove Oxidation
Step 5: Wipe Off the Sandpaper Grit
Repeat wet sand and wipe off the sandpaper grit until all heavier oxidation is removed, leaving only a light haze just from the 2000 grit sandpaper.
Step 6: Apply Meguiar's to Headlight and Rub Out Any Haze
Step 7: Let Meguiar's Dry Then Wipe Off...Congratulations, You Did It!
Repeat Meguiar's application, rub, dry and wipe off till headlights are clear to your liking. Once your headlights are in good condition, keep them that way by at least annually, wash, apply Meguiar's, rub off any haze, let Meguiar's dry and wipe off. Meguiar's is good on the car's paint as well. Other liquid combo polish and wax brands work too, such as Toyota Sealant Cleaner and Mothers Cleaner Wax.
Step 8: Other Instructables I've Written
Quick Fix Missing Petal on Steamer Vegetable Basket
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maniacse made it!