You can check in at the airport for free. The ticket counter opens 2-3 hours and closes 40-60 minutes before departure, for short domestic flights from smaller airports it is usually open for about an hour and a half and closes 20-30 minutes before departure.
Online check-in can be done 24 hours before departure, and boarding passes can be printed either at home or at an airport kiosk.
If you're travelling without luggage, it's definitely worth downloading the app (https://www.airnewzealand.co.nz/air-nz-app), which allows easy mobile check-in. Just scan the QR code at the airport.
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