Once you're through immigration and in the main arrivals hall, find a bank-branded ATM - not a currency exchange kiosk, and not one of those standalone ATMs with no bank name on them. The difference in exchange rate can be 10–17%.
What happened in New Zealand
At Auckland Airport, there's a Global Exchange counter right in arrivals - very visible, very convenient. I tried to use it and the rates were poor enough that I walked past it. Just outside the main arrivals doors, there's an ANZ bank ATM. Same location, completely different rates - much closer to the actual exchange rate.
The rule: walk past the exchange counters, find the bank-branded ATM, and use that. It's almost always just a short walk further.
Don't immediately doubt your card if it doesn't work. The first failure is usually the ATM itself, not your card - especially with standalone or generic ATMs. Try a different bank's ATM before assuming your card is the problem. Cards from major banks with a Visa or Mastercard logo work in most countries without issue.
Always pay in local currency at the ATM prompt. Some ATMs will offer to convert to your home currency for you (Dynamic Currency Conversion). Always decline - choose local currency. The ATM's conversion rate is far worse than what your bank charges. This applies at shops and restaurants too.