To live and work in NZ, you have to qualify for a visa. There are several ways of doing this, and this link
http://www.immigration.govt.nz/migrant/stream/work/ is the first step into the Immigration NZ website, where you can find out about them.
When you've had a chance to look around the various pages, if you have any questions, post a link and people will do their best to help.
If you have all the professional qualifications as a chef, you could apply directly for a Residence visa under the Skilled Migrant Category, without needing a job offer. If you get a job offer from a NZ employer, an application under SMC would be prioritized, and/or you could get a work visa, which can be processed more quickly.