If your partner is applying for a visa, be it as a visitor, worker or a resident, or they are already a New Zealand citizen or have a residence visa you may be able to gain a visa yourself. The conditions placed on them such as the length of their visa will also apply to you.
The main issue for partnership visas of any type is that you need to provide solid evidence that your relationship is genuine, stable, you have been living together for at least 12 months and that the person you are applying under is able to support your application. Many documents are required as proof, and you need to discuss what is acceptable proof with your immigration adviser. These can include a wide variety of evidence such as bills in both names or separate names to the same address over at least 12 months, mortgage agreements, wills, insurance policies, social media posts and photos of gatherings and formal certificates such as marriage or birth of children.