Most of Air NZ's groundstaff are employed by an internal company of the AirNZ Group called "terminal Services". Have a look for them in the phone book.
I know they hire students over the school holidays at the domestic terminal as ground assistant's, doing meet and assist's for passengers, delivery and collection of unaccompanied minors to/from aircraft etc...
The other thing is to go to the Domestic Terminal and introduce yourself to the Duty Manager (there's always one of them there) and ask about how you get a job there. That's what I did when I was made redundant from the bank and was looking for part time work whilst the bank paid for my instructor rating
Got a job the next day after speaking to the DM.
Other option, as the others have already mentioned, check out the " About Us" link on the main web page and click on "careers"
Good Luck
S2K