To apply, you can go to the German Embassy in Wellington. You can also apply at a local immigration office in Germany within 90 days of arrival, however, please note that in some centres (e.g. Berlin) wait times for an appointment may exceed 90 days, in which case it is advisable to try to secure the visa before leaving New Zealand. You can also apply at a local German embassy or consulate general in another country, if you are normally a resident of that country.
For more information, go to the German Embassy in Wellington website(external link).
For enquiries once you are in Germany, contact the local Ausländerbehörde (foreigners' office) in your town.