How to clean a hazy head light (on a honda) without buying an expensive polishing kit?

I have seen the kits by "Moms" etc. But they are really high cost… Any other solution to cleaning the light? Any kind of oil or such that would do it?

White toothpaste has just the right abrasion to polish the plastic

Cheap basic paste tooth paste and for me a drill with a pad.

Rubbing compound or plastic polish cost $5. Old T-shirt is free.

http://www.walmart.com/...90&veh=sem

Whitening tooth paste as stated. Somtimes though, uv rays fog the lenses out through and through. In that event, there's no helping it.
dremmel motor or drill motor with a buffing pad does quite nicely. Larger the pad, the easier and more even the app will be.

Depending on how bad the fogging is you can use polishing compound or pumice and water mixture. You still need something like a buffer for waxing a car to apply it. Trying to buff it out by hand is a joke.