Remove surface dirt
Pour ¼ cup of dishwashing detergent into a gallon of water. Swish it well with hands to mix the detergent in the water before soaking both headlights into this solution for a few minutes. Wash the lights thoroughly after a while to remove the surface dirt and any other loose gunk. Pat the headlights dry with a soft dishwashing towel.
Mix Toothpaste and baking soda
Make a mixture of toothpaste and baking soda by mixing the two in a 3 to 1 ratio, i.e. three parts of toothpaste and one part of soda. Make sure the paste is mixed thoroughly to form an even creamy texture. Apply this paste to headlight glass using a non-abrasive polishing cloth. Rub the polishing rag on the headlight glass in small circular motions. You will soon feel the oxidized particles breaking up, leaving colour on your rag. Keep rubbing the headlight glass until all the grime is gone. Thoroughly wash the headlight with soapy solution before rinsing and drying.
Treat the polished surface with water and baking soda
Mix half cup of baking soda in a gallon of water and wash the polished surface thoroughly with it. Rinse it well under an excess of tap water and dry with a clean, soft towel. Your headlights should be very clear now.
Repeat this procedure for the other headlight as well.