Don't bother with polishing kits, most of them just scratch the headlights unless you're very careful.
Wash the headlights to remove insects, dirt, and grit and let them dry.
Spray WD40 on a piece of kitchen towel or soft cloth. Turn the towel/cloth frequently as you polish the headlight lens using a circular motion. Spray more WD40 on as you turn the cloth. You'll notice a dark stain on the cloth/towel as you polish.
You can also use the same technique to erase marks from car bodywork that has been damaged by sun-tan lotion, make-up or hand-creams. Go gently and you'll need more than one "go" at it.