It is possible to go to school for up to 3 months without prior application, so-called tourist visa. Language schools There are almost places where acceptance from 1 to 2 weeks is possible, so you can also make use of a small break.
A school of language school longer than 3 months (13 weeks) can go to a student visa. If you are a school that meets the conditions of your current school quality, you can also work part-time. Also, as New Zealand can extend the visa in the country, it is also very free to think about extending your school entry period and proceeding to the destination of language study.