Here is a before and after of a 5 step solution I used on my mom headlights.
1. Sand with 600 Grit Paper (spent like 15 min, tryna get them perfectly sanded)
2. Sand with 1500 Grit Paper (spent like 15 min, tryna get them perfectly sanded)
3. Polish with No. 7 Brand Polishing Compound and Mothers Powerball Mini (spent like 15 min on each light, tryna get them perfectly clear before the Plastix)
4. Polish with Plastix and Mothers Powerball Mini (about 5 min per light)
They still look as good as when I did them, and I haven't touched them up.
Sanding is the way to go, remember sand it evenly working up the chain of higher number grits. You might have to start with a lower grit then 600 (maybe a 220-300 range). Always wet sand, it makes it much easier, and it keeps the dust way down. Get a good high speed drill to polish it with too, the powerball works best on high speed plug in drills rather then cordless. Work the polishing compound (under 3 bucks) till the lens is almost 100% clear, then wash the lens with dish soap. Then move over to the plastix, I find the plastix is a better finisher to provide just a little more gloss. Then use a good protective wax on it(I put about 3 light coats on).