it depends what country you hold citizenship or permanent residency in.
If you are a New Zealand or Australian citizen or permanent citizen, you can usually entervisa-free and stay indefinitely, as well as work and study.
If you are from the UK, you can usually enter New Zealand visa-free for six months, as long as you don't work at all and you don't study for longer than 3 months.
For the following countries, it is the same as the UK, except you only get three months:
Andorra, Argentina, Austria, Bahrain, Belgium, Brazil, Brunei, Bulgaria, Canada, Chile, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hong Kong, Hungary, Iceland, Ireland, Israel, Italy, Japan, Korea (South), Kuwait, Latvia, Liechtenstein, Lithuania, Luxembourg, Malaysia, Malta, Mexico, Monaco, Netherlands, Norway, Oman, Poland, Portugal, Qatar, Romania, San Marino, Saudi Arabia, Singapore, Slovakia, Slovenia, South Africa, Sweden, Switzerland, Spain, Taiwan, United Arab Emirates, United States of America, Uruguay, Vatican City
For all other countries, if you want to work or study in New Zealand, or you have any criminal convictions or have been deported from any country, you will need to apply for a visa: contact your nearest New Zealand embassy.