Take it from someone who had heavily hazed headlights: Don't bother with the "Plastic Cleaner" or any type of plastic polish. They simply do not have heavy enough abrasives to remove the hazing.
If this is the first time you've done this, it isn't the plastic itself that has hazed. The lights come with a coating that is intended to protect the plastic from UV and debris damage. The coating is what has hazed and must be removed. Wet sanding is the best way to renew your lights if they are heavily hazed.
What you will need:
A bucket of water
Misc. sandpaper in the following grits: 200 (optional), 400, 800, 1000, 2000
Rubbing compound (usually red)
Polishing compound (usually white)
Clear coat w/ UV inhibitor
Begin by dipping your sandpaper in the water and sanding the lights. Begin with the roughest grit (200 or 400) and sand in one direction periodically dipping your sandpaper in the water to rinse/renew it. After a good sanding in one direction, switch and sand exclusively in the other direction. When the light is good and milky looking, switch to the next highest grit and repeat the process. Sand the light in this manner up through the 800 or 1000 grit.
Now you should be ready for the clear. The light will still appear cloudy. Don't worry, this will disappear when the clear is applied. Clean the light with a lint free cloth and water. Spray several light coats of clear, allowing each coat to dry thoroughly.
After several coats are on, wet sand again. This time starting with the 1000 grit, then moving to the 2000 grit. Be extra careful not to sand completely through the clear you've applied. After wet sanding with 2000 grit, move on to the rubbing compound. Once that's been applied and removed, move on to the polishing compound. When finished, your lights should look as good as they did new.
You can probably skip a few grits and maybe the rubbing compound that I've listed. But if you want truly stellar results from your work, use all the steps.
