The Governor-General has an important role in the formation of a government after the election. He doesn’t decide who is going to be the government, or who is going to lead it as Prime Minister. His role is to appoint the next government, based on which party or grouping of parties will be able to form a majority in Parliament when it meets again.
Under our MMP electoral system, parties often need to enter into coalition or support arrangements with one another to get a majority in Parliament. The Governor-General will wait for party leaders to make public statements after the election, setting out the makeup of the next government.
In the days or weeks immediately after the election, the current government will remain in office as a “caretaker government” until the new government is sworn in. The normal business of running the country carries on, but significant decisions are deferred or only taken after consultation with other parties.
Once it is clear that a government can be formed, an appointment ceremony will be held at Government House. The caretaker Prime Minister and Ministers will resign (even if a similar government to the current one has been elected), and the Governor-General will appoint the incoming Prime Minister and other Ministers.
The Governor-General gave a speech in November 2013, in which he talked about his role in relation to the government formation after an election. If you would like find out more, you can read the speech here http://gg.govt.nz/content/press-gallery-dinner.