Legal academic Dean Knight discusses the difficult process of government formation on Radio New Zealand National (MP3). Dean quotes Sir Michael Hardie Boys' speech from May 1996 on government formation under MMP:

My task as Governor-General is to ascertain where the support of the House lies. In an unclear situation, that may require me to communicate with the leaders of all of the parties represented in the new Parliament.

Once political parties have reached an adequate accommodation, and a government is able to be formed or confirmed, I expect that the parties will make that clear by appropriate public announcements of their intentions. At that point it may be necessary for me to talk again with some party leaders. I would then expect to have sufficient information to be able to appoint a new Prime Minister, if that were required.

Throughout this period of negotiation, the incumbent Prime Minister will remain in office, governing in accordance with the caretaker convention.

That's the basic principle. The Cabinet Office has more.