Hi LeonC, welcome to Surfing Waves.
New Zealand is a great place to surf, where are you learning? Let's see if we can help you with your questions.
I have a 7'6 board. Am I supposed to duck dive with a board this big or am I better off turtling?
7'6'' is a big surfboard, and while it is possible to duck dive this board you will need to have some weight behind it. You are probably better at trying yo perfect your turtle roll. If you are trying to duck dive you will need to push down further towards the nose of your board, really sink it and use your back foot to get the tail of your board under the wave.
What is the secret to getting out back where all the nice waves are breaking??
Being fit, good at paddling and being able to duckdive or turtle roll well.
Fitness is something that you can work on when you are away from the beach - the other two just take practice. The road to becoming good at paddling out can be a long one. It may help if you watch other surfers before you paddle out. They may be more experienced than you and know the beach better (using rips - knowing the best paths, channels) and as a result be picking the best spots to paddle out. Remeber the golden rule while trying to improve any aspect of your surfing - Practice Practice Practice.
I find that it's hard for me to catch a green wave. They either flip me over or they just pass under me, despite me paddling like a madman.
The bigger the board the harder it is to get up to speed. It may help if you sit a little further out than you are normally and start paddling into the wave a little sooner. If you are constantly getting flipped over you could be lying too far forward on your board - try adjusting your position. Another tip to stop you going head first is just before the wave is going to take you start turning to paddle along the wave, not just straight forward - this should help stop the nosedive.
The wave you have described here sounds like Sumner in Christchurch - that wave always seemed to be messy to get out and hard to catch.
Hope this helps, let us know how you get on.