As a professional detailer this is what we do:
Sometimes depending on the condition of your lights u might or not sand... sanding its a bitch so removing your sanding marks can be a problem. If you think u dont need sanding just jump to step 2.
1- SANDING - If you want to sand or need, start wet sanding with the least aggressive paper like someone said 2500 will be fine if that doesnt quite cuts jump to 1000 (Even 800) then 2000 (1000 if you used 800 before then 2000) and finish up with 3000. I know this is a lot of sanding but that way you can deminish your sanding marks from being so agressive..and will b more easy to remove after.
Sand as much old and crappy clear coat you have on the headlight..be carefull with pressure on your fingers..use a backing foam plate or anything in between your hands and paper so you can apply even pressure.
2- COMPOUND - After u sand, clean it and dry it, u will notice it will b cloudy..Grab some compound with a would pad, if you have access to a drill which I recommend use it (it will b easy, fast and best result)..but be carefull with your speed as you can burn the plastic quick, work compound until you dont see much sanding marks...you will notice from the first pass that your headlight are coming clear again. We usually do from 2-4 entire passes to ensure we dont leave any sanding marks, the key here is the heat combine with compound what does the trick to eliminate your sanding marks.
3- POLISH - Now polish will bring that glossy finish to the plastic, u can use a sintetic wool (yellow color) or a foam pad (White most of the time) get some polish and start polishing 1-2 passes will b fine..if u want more shine..give another pass with another softer foam pad just to create heat and even out the glossy (Not necessary)
4- SEAL - By step 3 you are done, but if you dont put a protective coat on it..they will turn yellow in a matter of time (4-6months) so you might wanna grab a plastic sealer...we use OPTICOAT 2.0 which is a coat that can be apply on your plastic healights or paint (dont apply it if you dont know how) apply 2-3 even coats and that sholud give u at least a year if not more of clear headlights. For maintanance and longer protection..wax em one in a while so contaminants wont break your coat as easy and fast. DONT USE CLEANER WAX which will cause ur coat to break sooner, so use a canauba Paste wax.
Ill try to do a quick Vid for you guys to see how we actually do it...if you are interested let me know..so I can give u more Car Care Tips.
Thank you all
