You could always start with the cheapest and readily available compound - toothpaste! If that doesn't do the trick (and leave your front end smelling minty-fresh to boot) then Meguiar's makes a clear plastic polish/cleaner that you can try. It will help but if the lenses are too far gone, then you can go with something more aggressive. Get some progessive compounding, say starting with 1,200 grit - then 1,500 grit - 2,000 grit and so on.
If after all that you STILL aren't back to crystal clear lenses, then you'll just have to bite the bullet and replace. Hope this helped.
I had my headlights buffed out by an autobody shop. It probably took him all of 10 or 15 minutes. They look brand-new again. After that, I applied 3M Paint Protection film over them. They'll look brand new forever.
I understand, however, that the kits you can buy are also very good.
Before you pay a mechanic to do this... Go to AutoZone or Advance and pay 19.99 for the DIY kit that gives you all the rubbing compounds and sand paper you need AS WELL as the SEALING COMPOUND. Just ask for the "headlight cleaner" they should know what it is. This is a real common problem here in Florida.
DO NOT GO AFTER THE HEADLIGHTS WITH A COMPOUND AND THEN NOT SEAL THEM, THEY WILL ONLY DISCOLOR AGAIN AND BE WORSE NEXT TIME.
If they are SOO bad that the yellow is obstructing the entire light, replacement may be the only solution anyway.
I have had alot of good results with the mothers powerball. Its about 20 bucks and attaches to any powerdrill. Grab the mothers power plastic polish as well. Should take you 10 minutes. Of course, if the yellowing is on the inside of the lense, your screwed.