Hitchhiking around New Zealand is arguably the best way to get about the country on the cheap, but also a great way to meet locals. You'll hear time after time from the local Kiwis who stop for you that they used to hitchhike back in their heyday and are now returning the favor.
No signs are required for hitchhiking in New Zealand, using a thumb is sufficient to entice a driver to stop for you.
A fire truck might stop for you if you are hitching
The two competing bus companies are InterCity and NakedBus. One might be a bit cheaper than another but they both provide the same level of service.
A more expensive alternative to buses, but with service to fewer locations.
Buying/Renting a Vehicle
It is common for foreigners backpacking around New Zealand to buy a vehicle during their stay. Hostels located in the big cities like Auckland, Wellington and Christchurch will keep a collection of advertisements of cars, camper vans and station wagons for sale from individuals.
This website provides a guide on how to buy a vehicle in New Zealand.
With a vehicle of your own, you can travel about much easier, allowing for more fishing time. But having a vehicle will make your trip more expensive and could prove to be a headache if you have any breakdowns.