Here's what your supplies should look like.
I recommend using the mothers restoration kit, although there are others on the market.
Tape off any body panels surrounding the headlight so you don't scratch your paint in the process.
Attach Mothers Powerball to your cordless drill.
Apply quarter size application of Mothers restoration solution onto powerball. Set your drill to its lowest speed and begin to polish the headlight. Reapply solution as needed.
After each application wipe the surface down with the microfiber towel included in your restoration kit. You will see at this point if another application is needed.
Repeat the process for the other headlight.
Remove the masking tape and enjoy your newly restored headlights.