Do I need a visa to relocate from New Zealand to Sydney

I know to visit Sydney from New Zealand you don't need anything special. New Zealand passport holders are granted what's called a Special Category Visa (SCV) upon arrival, as long as you present your valid passport and a completed and signed incoming passenger card (handed out on the plane or ship over) you can visit Sydney without any other kind of visa.

Same goes for relocating from NZ to Sydney. If you get an SCV, as Stephanie mentioned, then you have the right to remain in Australia and work in Australia as long as you remain a New Zealand citizen.