I am aware there are many other questions like this one, but from what I've seen the answer varies significantly based on which countries are involved. I'm a freelance contractor in the US, and I may soon be working with a New Zealand company. What are my tax obligations? I know of those intrinsic to working as an independent contractor in the US, but what changes or is added when the client is in New Zealand?
US taxes are based upon US INCOME. Where that income originates is irrelevant.
You live and work in the US... you drive on US roads... your children (if you have any) go to US schools... you pay US taxes on all money you earn, even if that income originates from outside the US or even Earth.
In many respects, as an example, it's similar to state taxes. If you live in State A you pay State A taxes on your income, even if you have a client living in State B. You don't pay taxes in State B just because a client happens to live in State B.
The only difference with overseas clients is the rate of exchange for the currency. If you charge $10 US the client sends you $10US, that means they are actually spending roughly $15 NZD. You still earn $10 US dollars though. So you pay taxes on the $10 US dollars you earned.
So, in this case, don't let the client talk you into receiving NZD... you'll make less. Make it clear that all invoices are in US Dollars. If you don't and the client sends you that $10 as NZD, you'll only earn ~$7.
And yeah.. hire an accountant. Or even just find one you can connect with from time to time to bounce stuff off of if needed.