I'm in Japan, not NZ, but the system here is similar to what grandparent described. In over 10 years here I have never needed to do anything more than to sign

I'm in Japan, not NZ, but the system here is similar to what grandparent described. In over 10 years here I have never needed to do anything more than to sign a couple of forms provided (and pre-filled-in) by my employer, once a year. If you make only the equivalent of U$400 in extra income, there's no need to declare it. I think the cap is around U$2000. If you own a standard investment account, your broker will automatically levy taxes on your dividends and capital gains (rates are the same, BTW). You can still open a different type of account if you want to pay the taxes yourself. But if you're just investing for retirement and going buy-and-hold-forever there's little reason to do so.