Unlike Australia, New Zealand does not make all travelers apply for a visa before arrival in the country. If you plan on staying for three months or less and will not be working (which includes WWOOFing or any other schemes where you receive something in exchange for work), and you are from one of the visa-free countries, you can simply arrive in the country and have your passport stamped with a three-month visa. If you intend on working or staying for an extended period of time, you must consider other options.
I chose to apply under the United States working holiday scheme. New Zealand has a different scheme for all countries that are eligible for working holiday visas, which sets out the requirements for applicants as well as the term they are allowed to stay in the country. Most schemes allow travellers to stay in New Zealand for one year with the notable exception of the British working holiday scheme, which allows travellers to be in the country for up to 23 months. Applying for this visa was exceedingly easy--all I did was fill out an online form with my details and history (which was mainly health & criminal record questions) and within a day, it was granted. In addition, my visa fee (which I expected to be about $120NZ) was completely waived! The only downside to the visa is that once it is issued to you, you are never allowed to apply for another working holiday visa again. Therefore, I feel that I wasted mine as my plans changed after my visa application was made, and instead of working and traveling around the country for six months as I originally intended, I only traveled for 10 weeks. However, it gave me piece of mind that if I got in a bind and really needed the money, I could legally work, and if I ended up staying in New Zealand for a prolonged period of time because my Australian work visa took a while to be approved, I wouldn't have to worry about becoming an illegal immigrant.
The other main form of visa that travelers in New Zealand could be interested in are work visas. These visas allow you to work on a more permanent basis, rather than taking short-term work in agriculture/retail/etc. However, there are much more stringent requirements to be granted one of these visas; the most important of these is whether your chosen occupation is on the list of "occupations in demand" in New Zealand. The one that I find most interesting is the work-to-residence visa, which allows you to work temporarily in hopes of later becoming an NZ resident. I met at least two backpackers that plan on returning to the country and doing just that!
This was just a quick overview of the many visa opportunities that New Zealand has to offer; the main NZ immigration website has many more details than I could ever explain with my limited experience with the subject!