There are direct flights to Wellington from Melbourne, Sydney, and Brisbane/Gold Coast. From other cities you would likely fly either via Auckland or Christchurch, or via Sydney. Flight time from Sydney to Wellington is around 3:15 hours (but 3:45 hours the other way due to headwinds).
From USA and Canada
There are no direct flights from North America to Wellington. Air New Zealand flies to Auckland from Los Angeles, San Francisco, Houston, Vancouver and Hawaii, and many other other airlines operate direct or code-share routes to New Zealand from destinations in the US and Canada.
Skyscanner and other sites are useful at identifying route options.
Flight times to Auckland are around 9 hours from Honolulu, 12-13 hours from Los Angeles or San Francisco, and up to 15 hours from Houston.
From UK and Europe
Expect to spend at least 24 hours getting to Wellington. You will have to stop at least twice, once on the way to NZ and once in Auckland. Typically, flights to New Zealand leave from the major hub airports in London, Paris, Amsterdam etc. Skyscanner and other sites are useful for identifying routes.
You will have the option of flying either via Asia or via the USA. If you fly via the USA, you will likely stopover in Los Angeles, possibly San Francisco. You will need to get off the plane, go through US immigration processes, then get back on the same plane and fly to Auckland. Note that your luggage will stay on the plane. You will need either an ESTA or a transit visa depending on your circumstances.
Via Asia you will likely transition in Hong Kong, Singapore or Kuala Lumpur. Singapore’s Changi Airport routinely wins awards, but all Asian stopovers are fine.