Hi guys, first post.
It really depends how bad the hazing/oxidization is.
I've restored several sets of headlights in the past few years that have been badly oxidized (cloudy and yellow).
Generally what needs to be done, is the haze/oxidized plastic needs to be removed - cutting compound may work, but it really does depend on the severity.
I've previously started with 5-6 sheets of sandpaper ranging from 400-2000 grit.
Mask around (or remove) the lights and start wet sanding the lights with 400 until all yellow/haze has been removed. Note: they will probably look worse than before.
Then continue to sand up through the grades and you'll notice the light will slowly become more clear. Once you've hit 2000 grit, the light should look 'ok' and shortly after you should be able to hit it with cutting compound. Several attempts at this, then a cut and polish, finished with a wax and your headlights should look as new.