Originally Posted by NutHug

Errrr no. Punching is really easy.

What dubby said.
Rotate your body in one direction and then counter rotate it. Make sure your legs are on the ground and not moving so you can get more power out of your rotation.
When you are punching you will be standing on one leg and use the other one to either balance or boost even more power into it (or preferably both).
In the provided replay I'm standing on my left leg and extend the hip. By extending the hip (in combination with the glute) I'm pushing the leg into the ground which makes me rotate in the punch direction in gives therefore more power.
The other hip is contracted. By counterrotating the other hip I'm adding to the power of the move and I'm also using it to not fall to the left. The key to a punch is a solid base of your legs. The more they will rotate but stay at the same place, the more power will move into the spin of your body.

Sounds more complicated than it is. Spread your legs, rotate your body, counterrotate everything to punch.