June 2012: We are now officially Kiwis, we now have citizenship after living here for almost 6 years. To apply one must have lived in NZ and possessed a permanent residency visa for at least 5 years. The cost of the application is $470.
If you have broken the law (including speeding tickets), these can way against you. I got my acceptance 2 weeks before Terri, because she had to sort out her speeding tickets in the last 2 years, more than 2 or 3 and she would have to postpone her application.
You can obtain the relevant application forms from here: http://www.dia.govt.nz/Services-Citizenship-Citizenship-Application-Fees-and-Forms?OpenDocument#three.
After filling out the forms, you then make an appointment to see a case officer.