The majority of modern cars have headlight lenses made out of clear plastic. The harmful effects of sun, environmental chemicals, dirt, sand and other debris can yellow the lenses over time. You could take your car to the dealer and have them restore the lenses or buy new headlight assemblies, but there are a few much less expensive ways to clear them yourself in a short period of time without harsh chemicals.
A variety of kits are available that contain all the items you need to clear your headlight lenses. Look for these at your local car parts shop or in the car department of discount retailers. Always choose a well-known brand name -- this usually assures that you will have quality products that are made specifically for the task. Since these kits contain abrasives that you will use to polish the plastic, mask off the headlights with painter's tape and remove nearby trim before you start to avoid scratching any other area of the car. In addition, follow up the polishing with a good coat of car wax to prevent the damage from recurring.
You can buy headlight cleaning materials at DIY shops. Buy wet sandpaper in 600, 800, 1000 and 2000 grit. Start with the coarsest 600 grit and soak it for about 15 minutes in a bucket of water with a few drops of washing-up liquid. Sand the headlight lenses in a circular motion. Dip the sandpaper in the water frequently, keeping the sandpaper wet at all times. When there is no longer any residue accumulating on your sandpaper, move to the next finer 800 grit. Soak it for 15 minutes in the soapy water before beginning. Follow the same routine -- circular motions until the residue does not accumulate any more on the sandpaper.
Move on to the 1000 grit sandpaper using the same procedure. Then use the 2000 grit. This will take some time, possibly a couple of hours per headlight, depending on how foggy the headlights are. When you have finished, wipe the lens dry with a paper towel. You may see some clouding at this point, but the next step will clear that. Finally, get some rubbing compound and use it as directed. This will remove the clouding and finish the polishing job. Follow up with a coat of car wax to protect the new finish. Don't an electric sander or buffer for this job. The friction generated from the motion of these machines will cause the surface of the lens to melt and ruin the lenses.