Hi Donna,
There is just one major airport at Auckland ,but there are two terminals.One for International and the other for Domestic flights.
Taxis, as well as shuttles and bus's, are plentiful from both,but as Jim says above , I suggest you look out for the Co-op (Auckland Co-operative Cabs) or Corporate Cabs.They are up to standard and many Hotels will only allow these taxi's on their forecourt.