How to get New Zealand citizenship
If your parents are not New Zealand citizens, you are likely to seek citizenship by grant.
You will need to be on a New Zealand residence-class visa for at least 5 years, spending a minimum amount of time each year and over these 5 years, in order to be eligible for New Zealand citizenship.
Can I keep my other citizenship?
While New Zealand has no issues with dual citizenship, this may not be the case for your home country. There are many countries that will cancel your citizenship if you adopt another country's passport. Other countries are somewhat a bit more flexible and an official request must be made if you wish to retain your home citizenship, before you seek a New Zealand passport.