We now have a proportional representation system, so it is not as simple as it used to be, but we find it works quite well.
Here's how it goes: We have 120 seats in Parliament - 69 Electorate seats, (62 General - 7 Maori) and 51 List seats. The Electorate seats are filled by straight First Past the Post elections held in each of the 69 electorates which are determined by population so that each electorate has roughly the same population.
One quirk of the NZ system is caused by the fact that the Treaty of Waitangi is our founding document in which Maori sceded sovereignty to the Crown. As a result of the Treaty, Maori have 7 seats in Parliament that represent the Maori people. Thus in any one town or city, a person may be enrolled in the general electorate or the Maori electorate, and thus can only vote for one of the two electorates that represent that town or city. Only Maori people may enroll in the Maori electorate, but if they do they have no vote in the general electorate. This was to ensure that Maori received a voice in Parliament even though they are a small minority (now that is) of the total electorate.
The List seats are filled from each party's "Party List" (which must be published before the election) with the parties receiving the number of seats that represents their proportion of the "party vote". A party that wins at least one Electorate seat, or more than 5% of the party vote is elligble to receive list seats. The idea is that if Labour has 45%, National has 35%, and the Green's have 10% of the Party vote, then Labour should have 45% of the seats in Parliament, National 35% and the Greens 10%.
This percentage is made up of a combination of the Electorate seats won, and List seats. So for example if the Greens won 1 Electorate seat and 10% of the party vote, they would receive 11 list seats to bring their total to 12 (or 10% of the seats in Parliament)
On election day, each voter receives a ballot that contains the candidates for their electorate, as well as a list of registered political parties. The voter selects the candidate they wish to win their electorate seat, and the party they wish to support. These two votes do not necessarily have to be for the same party.
For example, you can vote for the Labour Candidate for your electorate, but give your party vote to the Greens. What this means is that people who support the Green party, but, knowing the Greens are unlikely to win a majority of seats, wish to ensure that the most electable left wing party does get that majority, can still have their votes counted.
Ever since we brought in this system, the Green party has recieved between 5 and 10% of the "party vote" ensuring that they had between 5 and 10% of the of the seats in Parliament. Before we went to MMP (Mixed Member Proportional) the Green party was never able to achieve any seats in parliament, even though up to 10% of the population voted for them.
So now we have how the MP's are elected. The next step is the Government itself. This is pretty standard. The party or parties (that is coalition of parties) that hold the majority of seats in Parliament (and thus the majority of votes) is called upon by the Governor General to form a Government. The leader of the majority party (or, by agreement, coalition) becomes the Prime Minister, and selects the Cabinet members.
The Governor General's role is pretty much the same as in Canada.
Bills are read in parliament three times. After the first reading they are sent to a select committee where public input is sought etc. The select committee then reports back to Parliament with any recommended changes, and the Bill is read again.
Parliament then decides whether the bill should proceed. At this stage Parliament gets down to the nuts and bolts and it is debated in detail and any amendments made to it before its final reading.
After the third and final reading to Parliament it is voted upon and, if passed, is signed by the Governor General and becomes law.
For detailed info on how it all works check out:
http://www.govt.nz/en/aboutnz/If you have any questions, feel free to ask :-)