When you are outside New Zealand you need to apply for a Visitor's Visa with travel conditions allowing you to travel to New Zealand.
When you are granted a visa on arrival in New Zealand (a stamp in your passport) you may remain in New Zealand for up to nine months. You will need to meet some requirements such as funds, health and character.
When you are already in New Zealand and wish to stay longer, you may need to lodge a further visitor visa application while your current visa is still valid, this is normally 30 days before expiry.
Please contact TNC for more information
Please note that you are not allowed to work while on a visitor visa, and you may study short courses up to 3 months max