Although the exact steps may vary depending on the kit, to use most headlight lens restorers you begin by washing the headlights and applying a clarifying or lubricating compound. You then buff them with sandpaper to clean off the cloudiness.
Be sure to apply electrical tape or some other easily removed protector to the paint at the edges of the headlights. If this step is missed, the sandpaper may scratch the paint. Read the directions included with the kit carefully for best results. Most kits require you to buff them out after sanding and applying, and may not include buffer pads. If the kit you buy does not have pads, try using a microfiber cloth.
The kit should include the proper type of sandpaper for sanding. Some include buffer wheels which attach to an electric drill, so read carefully before buying if you do not have a drill. Many require you to spend a bit of time buffing out the scratches and cloudiness. If you do use a drill, be careful and slow because using too much pressure or focusing too much on one area can cause damage.
Headlight lens restoration kits are designed for very cloudy and scratched headlights and should not be used on clear headlights. They can cause damage if not used properly, so be sure to inspect your headlights before you buy a kit.