Before we start, polishing your car is not the same as waxing your car. When you wax a car you basically give the paint an additional layer of wax, to improve the shine. Polishing is harder, more involved work, which entails breaking down the outer surface and working the polish into the paintwork.
There are two ways to polish a car, either by hand, or using a buffer. If you have never used a circular buffer, I would recommend you polish by hand, gain some experience with a buffer, on something that is not doing to become a problem should you scuff or gouge the paintwork.
If you intend to polish the car outside, do it on a bright day, but not in full sunshine. If you are working in a garage then a decent halogen light to provide adequate lighting should be used.
Use a good sized towel (kept just for the car), and fold it in on itself, ending up with a round segment being held in the palm of the hand, similar to a medium plastic ball.
Tape off any plastic, bumpers, trims, and wing mirrors. Polish in a circular motion, concentrate on small areas at a time, ensuring the polish has been absorbed by the paint and your shine is visible, before beginning the next area.
Although polishing is much harder work, the finish you can achieve is far superior to just waxing.