Step 1: Clean the headlights.
Step 2: Now run to the auto parts store
Step 3: And if you're lucky, you are done.
Step 4: What you'll need, and what to do
Items not shown cuz I did this a while back
Dip the 800 grit sand paper into the soapy water and start wet sanding the headlights in a circular motion, be sure to keep dipping the paper into the water. Do this until you get bored. Wash with clean water
Then step up to the 1500 grit, repeat.
Chuck a cheap cotton buffing wheel into your electric drill, and pour the Brasso into a shallow dish. Dip the buffing wheel into the brasso, and then start buffing the headlight, keep the wheel moving, you don't want to stay in anyone spot too long, and keep refreshing the brasso on the wheel, don't let it dry out. When you get really board with this, give up, no use being a darned fool about it.
At this point take a clean rag and wash the brasso off with the soapy water. Wipe everything dry. NOW use the plastic polish and, maybe you headlight will look better.
Now do the otherside.