I've seen a variety of how to restore headlights properly videos on YouTube and most of them look like they would not work long term so I thought I'd try it with a brillo pad and some water and then add a protective silicon coating over the lens after drying it off. It worked perfectly and the headlights are still clear today.
The brillo pad is just abrasive enough to get rid of the gunk on the headlight without scratching the surface of the lens.
It is no use just cleaning the headlights and not using a new protective coating as they will get very dirty again very quickly.
This is a quick and cheap method to bring your headlights back into tip top condition and most of what you need you probably already have in the kitchen. If not?
Get yourself some on Amazon.