I was almost certain there was a similar thread 3 months or so ago. Jiggered if I can find it though.
Sorted.org.nz should be your starting point as to the fundamentals of investing. If you want to invest in NZX listed stocks direct, ANZ and ASB offer on line trading platforms. If you decide to go down the managed fund or ETF route, good starting points are NZX Smart Shares, Rabo Direct and your existing KiwiSaver provider (and if you don't already have KiwiSaver, you should be investing the $1,000-odd minimum a year for $500-odd guaranteed returns - won't beat that anywhere). I've also met the guys that are starting up www.sharesies.nz - nice guys with a good idea to help people invest. They're in beta but you might want to have a look at that too.