Flat / Flatmates
Fatting is the most common way to spend a longer period of time in Auckland. Unfortunately finding a flat from abroad is not an easy task. A lot of people choose to live with a hostfamily or stay at a hostel for a couple of weeks. This enables you to check out different flats and possible flatmates on site.

The NZ Herald is THE place to find the right flat. Other than that you may want to take a look at:

flatmatesNZ
Flatfinder
Flathunt

Student Accommodation
In case you are coming to Auckland to study at any educational institution you may want to try student accommodation. The quickest way to meet other students, who in most cases will come from countries all over the world except NZ.

Princeton Appartments
Railway Campus


Homestay and Farmstays
The best option to practice the language and learn about the country's culture. Homestays offer great opportunities provided you get along with the family you are staying with. As a former US high school exchange student I can promise you that living with the wrong family is no fun at all. If you are old enough though, you may just want to give it a try. Moving to another accommodation option should not be a problem.

Hostel / Backpackers
If you want to meet different people from all over the world you may want to check out the Backpackers option. I have found very positive comments on the following hostels: 

Auckland International YHA
Auckland City YHA
Central City Backpackers
Auckland Central Backpackers
City Garden Lodge, Parnell
Bamber House, Mt. Eden