Summarize:

Spray your cleaner of choice liberally onto both headlights. Then, use a microfiber cloth or soft automobile sponge to wipe away as much dust, dirt, and stuck-on debris as possible. Giving your headlights a quick preliminary wipedown will get rid of the worst of the mess, allowing the toothpaste to work more effectively on what’s left. Once your headlights are clean, dab them with your towel or chamois to soak up any standing streaks or droplets of moisture. Be sure to dry off the edges of the covers, as well.  If you’re using a towel, make sure it’s of the lint-free variety. Otherwise, you could end up leaving behind small fibers, which can easily become stuck on the headlight covers. Alternatively, you can apply the toothpaste while the headlights are still wet to produce a bubbly lather similar to soap. Stick strips of automotive masking tape or painter’s tape over the paint at the top, bottom, and sides of both lights. Afterwards, inspect your work closely to make sure that there’s no exposed paint visible near the portion of the lights you’ll be cleaning. The gritty toothpaste, combined with the pressure of polishing, could potentially damage any paint that’s not covered with tape.
Wash the headlights thoroughly with glass cleaner or soapy water. Dry the headlights using an absorbent towel or chamois. Tape off the area around your headlights.