The main gateway in and out of New Zealand is Auckland International Airport.
Here is some information which may make your departure and arrival more pleasant.

Auckland Airport Rebuilt
The International terminal at Auckland has now been completed and all arriving and departing passengers are now on seperate floors. Arriving passengers leave their aircraft and walk along the bottom floor to the arrivals area. Departing passengers move along the top floor of the pier before descending down to their departure gate louge by escalator or stairway. In the new departing passenger area there are floor to ceiling windows to look out at the aircraft, new bars and cafes, a Burger King and shops.
For more details visit http://www.auckland-airport.co.nz/

Departing Passengers
When departing on an International flight, the minimum recommended time to check-in is 2 hours before your flight departure time. However, as Auckland airport now has so many things to see and do, you should save yourself any stress and last minute panic by checking in 3 hours before your flight.

Check you flight is departing on time here http://www.auckland-airport.co.nz/FlightInformation/InternationalArrivalsAndDepartures.aspx

Parking.
Short term parking for those who are seeing off friends or family is available directly outside the terminal. For people leaving their car while away on holiday, long-term car parking is the much cheaper option. When you arrive at the airport, follow the signs towards the International terminal (rather than going directly ahead into the carpark). As you drive past the front of the terminal you will see the long term carparks signposted.

When you pack
Make sure you put all sharp objects (such as pocket knives, nail files, knitting needles, razors, scissors, etc) into the luggage that you check-in. DO NOT place them in your carry-on luggage.

Dangerous Goods
Do not carry gas powered appliances, fireworks or any fuel (including camping fuels or Zippo lighter fuel) with you on the aircraft. If in doubt, phone the Aviation Security Service on +64 9 265 1700.

Before you leave home 
Phone your airline or use link above and confirm your check-in time. This will save you time and any hassle as different destinations require different check-in times. Check in on the Ground Floor of the International Terminal as soon as you arrive. Have your airline ticket and passport ready at check-in. If you need any assistance to board your aircraft, please ask your airline during the check-in procedure.

Go through the departure door on the first floor early. There may be large queues for customs processing that you cannot see.

In the Departure Area
Proceed through New Zealand Customs and Immigration. Have ready your boarding pass, departure card and passport. Pass through the security check-point. X-Ray machines used by the Aviation Security Service at Auckland International Airport do not harm exposed or unexposed film or data on computer disk. Passengers may request hand inspection - this may require you to open your camera and/or remove your camera lens. You may also be asked to demonstrate that your laptop computer is in working order.

Take advantage of the shopping opportunities in the airside shopping mall. Don't forget to collect your duty free purchases.

Note your departure gate number - all gate lounges are numbered, and the flight information of your aircraft prominently displayed. Monitor the departures board and go to the gate lounge in good time - not at the last minute.

Arriving Passengers
When you arrive back into New Zealand, be prepared to clear customs and to go through MAF searches.
As an island nation our borders are well protected and the Ministry of Agriculture and Fisheries (MAF) do a great job at keeping unwanted pests out. The main items of concern are food, wood/straw and plant materials (including souvenirs), seashells and animal products.

Avoid an instant $200 fine by declaring any items you are not sure of.
For more information visit the MAF website here.