If your invoice (product cost + shipping cost) is more than NZ$400 then you will have to pay GST. That's because Custom currently only collects GST on imports if the amount is $60 or more ($400 * 15%).
Some items may attract import tax as well (most electronics dont, jewellery and clothing do).
Notice that Customs may consolidate multiple orders arriving in the country to the same user and apply GST on the total. If you place multiple orders under NZ$ 400 to evade GST you may be caught on this. This is being discussed here.
You can can have an idea of how much you will pay using the Duty Estimator. If you have to pay anything then you will also have to pay a fee to the company doing the clearance on your behalf.