What sort of regulations do I need to understand before buying a farm?

Most environmental management issues are handled by the 16 Regional Councils in New Zealand.  Local councils are then responsible for land-use zoning.
Farming must be undertaken in compliance with a number of local, regional, and national regulations. These regulations cover land zoning and permitted land uses, animal welfare, land care, pest control and environmental impact, amongst others.
It's important that you understand all relevant regulations thoroughly.  Contact your local council or legal advisor for guidance.