There are plenty of places to rent cars in New Zealand starting at as little as $20 a day, though be sure to check the terms and conditions! There are rental companies based at all the major airports, but here are a few well known ones
If you are thinking about buying a secondhand car, check out TradeMe. It is fairly easy to do and there are some great deals to be had, but as everything is sold via online auction so the process could take over a week. Also, makes sure you get the car checked out (AA) unless you feel confident enough yourself to do it.