I bought a similar product as the first attempt on my headlight restoration : "Blue Magic Headlight Lens Restorer". TOTAL JUNK.

try #2 was another product from AutoZone that had a spinny pad thingey, was so disgusted I threw the whole thing away, so I don't know the product name.

try 3 : Meguier's Heavy Duty Headlight Restoration Kit : TOTAL SUCCESS !!! Highly recommended.
This and the top end 3M kit are similar, both contain different grades of sandpaper, polishing compound,
and a UV protectant.

FINAL STEP - when you get them all sparkly again, put some headlight protector films on them.
There are a couple of versions of these also, no particular recommendation.