From my research I was able to find that I would at least need to get accepted for a working holiday visa from the NZ government. Here
I can't imagine this would be the only requirement. I've been trying to figure out what documents I would need to complete for the US government, but all I keep finding is information about non-residents immigrating to the United States.
Also, if you've ever been to New Zealand for an extended period of time, any tips/suggestions would be appreciated :).