If you would like to visit to New Zealand on a short term say 3 months for family visit, holiday visit, medical treatment, short term study, short stay while flying through Australia you need Tourist visa or Visitor visa.
Visitor's Visas are valid for 9 months in an 18 month period. Under certain circumstances you may be eligible to extend your 9 month stay by a further 3 months. You must also be able to meet all health and character requirements to be granted a visa for your visit to New Zealand.