Most NZ surfcasters use the so-called 'Overhead' cast. Trouble is this cast, while being simple and easy to learn, is very inefficient. For an explanation of why it is so inefficient see casting technique on this site.
I am not going to attempt to explain how to do these casts, as the links above should get you started. But I have to write this warning: both these casts generate enormous power and will fling a sinker at great speed, the Pendulum cast even greater than the Off the Ground.
You must learn and practice these casts well away from other people, you can do very significant damage if your sinker hits someone.
You should learn the 'Off the Ground' cast first, and then proceed to the Pendulum cast.
If you can find a surfcasting club in your area, there will more than likely be some members to help you learn both casts.
It is also worthwhile to remember that firing casts out into the middle distance is not always the way to go. The old advise, 'fish your feet first', is good advise.