As always, I'm here to play devils advocate, with a word of warning/advice.
Keep in mind that those headlamp polishing kits are a very temporary solution UNLESS you apply a new permanent UV protectant after you have polished. Plastic headlamp lenses are coated with a UV protectant layer, and when you polish the lenses, you remove that protectant. Before polishing, the UV protectant is still working, even if the lenses are clouded it is basically all in the UV layer of the lens. When you polish, you remove the haze, but also the UV protectant layer with it. So you get a better looking and performing lens - but only for a short while. Now, without any UV protection, the lens will haze faster, and it will haze through the entire depth of the plastic new to just the top layer, which will become irreversible and no amount of polishing will clear the haze.
The only real solution is to:
1. replace the lamp with OEM units (and only OEM units - I have never seen an aftermarket unit that met the FMVSS requirements to be legal sold for highway use. Photometric, dust intrusion, fogging, thermals, they all fail, always) or
2. Apply some sort of PERMANENT UV protectant to the lens. Real permanent solutions aren't cheap ($50+ for Opti-clear, Xpel film, etc), but they are cheaper than a new set of OEM headlamps. Note: the Mequire's headlamp protectant from the autoparts store is not anywhere close to permanent, and I seriously doubt anyone is going to reapply it every week, and if you don't, you'll be back to hazy lenses in a year and you won't be able to polish them clear this time.
Source: used to do headlamp evaluation and design for automotive OEM.