How to go about getting a ride in New Zealand
Well, it all depends what you are looking for and for what kind of period. If you are travelling up to three weeks I suggest renting a vehicle.
Depending on what kind of vehicle you are looking for, there are several rental car companies out there. Check this website for more tips: https://www.backpackerguide.nz/the-best-campervan-rental-companies-in-new-zealand/ You can find rental companies in any big city that has an airport. So whether you are flying into Auckland, Wellington, Christchurch or even Queenstown, you shouldn't have a problem renting a car or campervan. Mind you, renting a car and especially a campervan doesn't come cheap. If you are travelling with more than one person, you can split the costs and then it's pretty fine. As a solo traveller it will cut a decent hole into your purse. So better start saving up for the ride early.
If you are a flexible traveller you might want to look into relocation options or transfer options. Some rental car companies often look for someone to drive a rental car from one rental location to another one. You might have to pay a small fee for doing that but it beats a regular rental price. The only drawback is that you are restricted on the time to get from A to B. So you might have three days to drive the car from Auckland to Wellington. This, however, is something the company will tell you so you know what to expect. I have heard of several people who have taken advantage of that option and they were very happy with that. I personally haven't looked into it so far.
Especially for longer stays in the country where you want to drive around a lot it might make sense to buy a car. The whole registration process is easy as, as the Kiwis say. You take the license plate number to the post office, fill out a form with the necessary information (your name, an address in New Zealand so they can send you the papers, the model and make of the car, your passport and possibly a phone number), and pay the fee, which in January 2018 was very low, only $9. You see, it's easy to register a car in your name. That's a reason why car theft is rising. You don't need any proof of having bought the car or who the former owner was. So, don't get your car stolen!
Now, the process of buying the car itself is a bit trickier. Actually it's easy too, but you have to factor in time. You can either go to a dealer where you get a certain warranty with your car. In order to find a dealer, you either google them online or you go to trademe.co.nz where next to private sellers also dealers advertise their cars. Some dealers even offer a buy-back guarantee as long as the car is returned in the same shape or at least similar shape to when you bought it. When I got my car, I got a 50% of my paid price guaranteed. You can of course try to sell it privately and get a few more dollars out it. That depends again on how much time you have to sell the car because it might take a few days to find a buyer.
Another option is various Facebook groups like backpackernz or similar names where other travellers are selling their cars/vans often with camping equipment included. Make sure you get a car where the WOF (warranty of fitness) is new to make sure the car passed a technical test. Also the REGO should be new or last a while. That's the fee you pay to the country for using their roads. It's the registration of your car for driving it. When you buy a car from a private seller, you have no warranty whatsoever. It's basically bought as is. So either you know a bit about cars or you test your luck.
In both cases price limits don't exist. Depending on what you want you can get a car for under $2.000, a van starting at about $2.000 and going up to $12.000 or more. It all comes down to age, equipment, and model. I strongly recommend self-contained campervans because you are allowed to camp almost anywhere. Self-contained means you have a toilet on board (and that can be a little porta potty, a portable toilet) and a gray water container. That means you are not dependent on public toilets and won't pee and shit in nature and people's gardens. Yes, that has become a huge problem in NZ and I understand that locals are literally pissed by campers' behaviour. I bought my self-contained van from a dealer and then equipped it myself with bedding, storage boxes, cooking utensils and whatever I needed to camp. All together I spent about $5000. When I sell my van after driving around for three months and I get $3500 back, I'll be very satisfied with that. If not, I'll take it back to the dealer and get my 50% back. Still fine by me.
Last tip with a car: get AA, the roadside service. Hopefully you'll never need it, but better safe than sorry. When you rent a car, check roadside service is included. When you buy a car, get AA yourself. Btw, AA does checks on cars too. That will get you an independent and objective feedback on the state of your potential vehicle.