The kit consists of their brand "Plastrx" clear lense treatment gel, a polishing head for use with a generic household electric drill, and a Meguire's super fleecy microfibre wipe.
The instructions are to mask off the lamp in question, apply a "Nickle" sized amount (they are an american firm!) of Plastrx onto the polishing head, apply evenly to the lamp surface and polish with the drill attachment as fast as you wish. Wipe away residue with the supplied microfibre cloth. Repeat until you see results you are pleased with.
I used 3M masking tape I already had in the shed.
I left about 30 seconds between treatments incase the lamp lense had heated up, but to be honest I don't think this treatment generated any heat which could have burnt the plastic lense as the polishing head is too soft - not an abrasive one.
I've got some pics below which show the difference before and after. It certainly has made an improvement.
I would certainly recommend this Meguire's kit to anyone who is a little daunted by taking varying degrees of wet and dry paper to their headlamps (like I was).
The Plastrx gel can also be used on other gloss plastics such as our rear licence plate surrounds and our dash instrument binnacle (although crucially it warns NOT to use it on Navigation displays) and seems a good treatment.
New headlamp:

Front - difference between old and new lamp lenses:

New lamp is of course immaculate:

Old lamp, trim already masked off and its scratched and aged appearance:

The Meguire's Kit:

Kit contents:

Polishing head attached to drill:

Applying Plastrx gel to the head - several applications were required:

Applying to the headlamp lense - again several applications were needed as it's a gentle polishing gel - not too abrasive:

Old lamp now shiny and bright looking:
