Meguiar's (sp) and other brands of wax/polish carry "plastic polish" that will do the job. Just follow the directions.
Good question and I think I heard once that you could soak them in vinager for a while to take it off. I've been meaning to try this but keep forgetting about it.
I recently did some, I sanded them lightly with 600 sandpaper and the cleared them. look good and should look good always with little to no maintnence.
Furniture polish and wax approaches work by optically filling in surface damage, with varying results. Plastic polish does the job by abrading away bad surface...if bad, you might want to help it by some very fine sanding. I once ruined a plastic gauge lens by cleaning it with carb cleaner, which instantly crazed the surface to the point that I couldn't even see the gauge needle. I had a tiny pack of ultra-fine sandpaper from a hobby shop, grits in the thousands, and applying that got the surface back down to clear very quickly.
that's the best way. that way you are sure to get out the larger scratches. i just did a pair, started with some 240 to knock down the lettering cast into the lens, then 400,600,1000,1500, and finally some 5 micron polishing cloth because i had it, then polish to a high gloss with some clear plastic polish. i have a su****ion that rubbing compound for paint would probably work too.
It will only polish off if it's really just on the surface. If you don't want to spring for the Meguires polish if they are a lost cause (I tried it on a convertible back window that was past polish and could have just saved the money to put toward a new window, it ain't cheap!) Try a spot with some Colgate or other "white" toothpaste. I use Colgate to polish carved stone sculpture! What Ray said are the steps to follow before the polish too. Are they really clear if you get them wet with water, or are they crazed through the plastic? I had crazed, as in cracked, tail lights on a '55 Olds and closed up 90% of it by "painting" them with some Weld-on brand water thin clear plastic/acrylic cement. Then polished them with toothpaste. Just don't spend $50 on polishing supplies trying to save lenses you can replace for $40
I use the same thing folks in the industry use: NOVUS Plastic Polish. They use 'em in everything from LEXAN factories to the iPod factory. I use it to restore old telephones, but it works on everything from getting scratches out of CDs to making headlight pods and motorcycle windshields look new. It's a cream, with grit in it. There's 3 kinds, light, medium, and heavy. You "go through the grits", just like sandpaper, and it'll look brand f'n new. ~Jason
Like Doc says, "Are they clear when wet??" I found that before trying any "magic compounds", a good scrubbing with some mild dish washing detergent and a stiff tooth brush, let dry, and see how they look. THEN move to the next step. If the surface (outside) appears to have a "haze" (possible over spray) after washing, then I use the tooth paste route. (denture polish is a bit more abrasive than regular tooth paste) A word of caution; some waxes will/can eventually cause a chemical reaction over time with the plastic, and make the problem worse.
I've always used Mothers metal polish also. Works great at removing plastic surface oxidation without discoloring, and leaving a smooth surface. I've used in on my plastic bakelite radios for years. Obviously it won't fix cracks and scratches.
best way i have found is to wetsand them with a very fine grit sandpaper, and re-clear them. as stated above. i have seen it done to headlights and tail lights, and they look better than new. they also have a better layer of protection and the shine and clearness should last a lot longer.
my method that i use a lot is to go over it with 600 1000 then 1500 grit sand paper and then hit it with the blue coral metal polish and a good powered buffer. makes them look like new and protects them from future oxydation. i charge about $200 to do that here at the shop, now you guys know my trick for free. just don't spread it around salt lake, the results have gotten some talk around town
I've used Blue Magic metal polish before on plastic with awesome results. It even restored a Paul's Boutique CD that was otherwise unplayable.
TOOTHPASTE!! used it on my dads '89 chevy's head light lenses ( typical 80's yellowing ) and it worked great. Washed first and used an old sweat shirt to apply. Took some work, but the price was right
I bought the buffing wheel and stick compounds from Sears, similar ones are sold through Eastwood Co. I use the white stick, and buff the lens with the cloth wheel on my bench grinder. Just keep it moving, because it will melt! They come out looking new. Or actually the outer surface has more of a "shine" to it than new lenses. It does a really good job. Try it, you will like the results.