So, steps I took on a car that had been outside in the sun for 25 years.
-Sanding with: 800-1,200-2,000-2,500-3,000 grit, all wet.
-Good cleaning with pure alcohol or general-purpose car cleaning spray (not just any cleaner) after the sandpaper.
-Polishes: I used one that came in a kit I had bought, then I used coarse Meguiar's (ultimate compound) and then again with Meguiar's fine polish for finishing (ultimate polish).
-Good cleaning, the waxes with clean cloths of course, etc.
-And finally, I applied K2 in two coats.
The results are amazing but you have to know what you're doing... K2 is for sealing... Not for polishing, etc., but for protection AFTER you do all the above steps.
The results speak for themselves.
For such a job and such a burnt headlight, it took me about 4 - 4.5 hours in a covered garage (you shouldn't work on hot surfaces or in the sun).
It's a nice DIY if you're not bored... If you don't do all these steps you might cause damage and it's better to have someone else do it for you!