There are multiple ways of coming to NZ for work. There are some differences between categories and it's important that you know which category you most certainly fit.
I believe that the fastest way of coming here for work, is via the "Talent - accredited employer" category. This is the category I used in coming here. Basically, the hiring company has to be an NZIS (New Zealand Immigration Service) accredited for you to qualify in this category.
It works very simply and like I said, it's one of the fastest, easiest and cheapest way to come to NZ for work. You can find more information from the link below:
Be sure to check out the list of accredited employers. Visit the company website and see if there are job postings there that you can apply and submit your application through there. Most companies will have job listings in their websites and the information on how to apply for them.
The company will contact you, usually via email, to arrange an interview with you or they may ask for more information about you or some referrals. The interview will usually be a phone interview. Take note that all of these correspondence between you and the company are off the POEA and OWWA's radars. The company might even send you here for a final interview, like what they did with me. It's easy, you just need a visitor's visa, which is free and again, you don't need to go through POEA nor OWWA for this.
Once the company will decide to hire you, they should give you a contract and working conditions document for you to sign. This is important as this will be needed when applying for the work visa. I will post separately regarding how to go about this.
There are also some good job search websites. One particularly popular here in NZ is www.seek.co.nz. Try searching here as well. Don't worry if you'll go through an agency, most of them take little commissions only and you can get out of the agency later if you can find a company that will hire you directly.