You don't need a kit.
Stage 1: Wet' n dry, with a bit of fairy in the water about 400 grade to start with, rub down by hand or use a block if you prefer. Move up to about 1200 grade to finish when the haze has gone. Rinse frequently
Stage 2: Apply T-cut wet and polish it in quite hard, give it another rinse
Stage 3: Apply polish with a soft cloth. I use Autoglym. Just keep polishing it until the polish "dries" and you rub all the residue off.
It is perhaps easier if you remove the headlamps from the car, but not necessary. Similarly, a machine polisher may speed things up, but I can do a 9-5 headlamp in about 20 minutes or so if it isn't too bad
Be brave