Have you made your booking with Air New Zealand through the website or over the telephone, you can view your booking online in order to manage. Having booked a flight ticket one can manage his flight to fly on the mentioned date and time, changing and canceling the tickets, reserve the seat and much more.
https://medium.com/@jhonnys60199212/unaware-of-the-air-new-zealand-ticket-cancellation-policy-e061eae67fa9