So here are some things to consider, young chickadees!
First, decide if you're going through a program or not. I'm told Bunac and Greenheart are good. What these organizations do is all the nitty gritties-- getting you a tax number, a bank account, a permanent address that will forward your mail to wherever you end up in the country, picking you up from the airport and giving you an orientation, and helping you find a job. It's expensive though, and everything they offer are things that can be done yourself, if you want to save the money.
If you decide not to go with a program, this is what you should be thinking about before you leave.
1. Bank accounts
One AMAZING thing about New Zealand is that you can set up a bank account before you go, which means your money is waiting for you when you arrive. I had the hardest time deciding what bank to go with, as they all seem pretty reputable and similar. In the end I decided to go with Kiwibank because they're entirely New Zealand owned. The customer service so far has been great. Of course, you can open an account when you get there, but it takes some time and some paperwork that you might not have (a permanent address, a utility bill, an IRD number), and that you won't need if you open it from abroad.
You'll want to consider the issue of credit cards. You can't pay an American credit card from a New Zealand bank. I'll be leaving some money in the States in a fee-free Capital One 360 account (I had to switch from Chase, which did have fees) to pay off my credit card if an emergency comes and I have to use it. I will mostly be using it sparingly, though. (UPDATE: I have just discovered that certain banks won't do international money transfers, Capital One included. Leave your old account open long enough to do the transfer to your New Zealand bank if you can - or else a Western Union FX account should work.)
2. Cell phones
If you don't care about your current phone and you don't mind buying a cheap one in NZ and then another one when you get back home, you're sitting pretty. I decided that I did want a new phone for traveling, and I wanted it to double as my camera so it needed to take good photos, and I wanted to keep it for a few years. Thus I entered the dark and disturbing world of international phones. To keep it short, every phone company broadcasts its signals on different network bands, and certain phones are only equipped to pick up certain bands. You'll need to do some research to see if the phone you want can pick up the signals both in your home country and in New Zealand. I've settled on the Sony Xperia, but the iPhone will likely also work.
3. Insurance
You're required to buy health insurance to enter NZ on a working holiday visa. So far it looks like Orbit is going to be the best- it's by far the cheapest, and seems comprehensive (though Kara and I are both bummed that it doesn't cover black water rafting...). They offer an option to pay a little extra to cover your belongings, and I may do this. However, because I'm subletting my apartment in the States, my renters insurance may cover my belongings while I'm overseas. You should look into this if you also have renters insurance and will be keeping it.
4. Permanent Address & IRD Number
This is a tough one! In order to work in New Zealand, you need an IRD number for taxes. In order to get an IRD number, you need to have a permanent address. You probably need to find where you're working before you can get a permanent address... and around and around we go. Kara and I bought permanent addresses through the backpackerboard mail service, which we're hoping will work out well. It will also allow us to give our family and friends only one address for the entire year; the mail service will forward our mail to wherever we happen to be.
5. Odds and Ends
You're going to need some adapters! New Zealand has "Type I" plugs. Don't forget them! Also don't forget to bring an outfit for interviews. Definitely don't forget to update your resume, and upload any important documents to the cloud. Bring a padlock if you're intending to stay at hostels. (I think you can rent them, but it's safer to have your own.) Bring a car charger if you're planning to drive. Change your home addresses on all of your accounts. Get a skype account. Get your phone company to suspend your service, if you want to keep your phone number while you're gone. Take a last trip to the doctor and get a few months worth of any prescriptions- and have her write a note for any prescriptions you want to bring into New Zealand.
Then there's a bunch of stuff that will only apply to your unique situation. Try to think through all the variables in advance so it doesn't all hit you right at once the week before you leave. Do you have things to put in storage? Do you need to find a subletter? How much notice should you give at work? Do you want to start a blog?? (Obviously!) Do you just want to create a bonfire of everything you own so you don't have to deal with it? (Yes.)
The process of preparing to go can be expensive, and trying to keep on top of everything is really discombobulating. Just keep on keepin' on- and keep in mind just what all this is for!