Wash the headlights with soap and water
Dry the surface completely
Tape off the area around the headlights
Apply toothpaste or a headlight cleaner
Rub the lens with a microfiber cloth in circular motions
Rinse and wipe clean
If needed, wet sand with fine-grit sandpaper
Use progressively finer grits while keeping the surface wet
Apply a polishing compound
Buff the headlights with a clean microfiber cloth
Apply a UV sealant or headlight protectant
Repeat maintenance regularly to prevent yellowing