By train
Tranz Scenic (http://www.tranzscenic.co.nz/) offer one daily service from Auckland to Hamilton departs 7:25AM, arrives 9:50AM, at $49 per person, one way. The journey takes an hour and a half, and isn't terribly exciting, but is much quicker than bus or car. There is also one daily service from Wellington to Hamilton departs 7:25AM, arrives 5PM, which costing $129, provides an opportunity to take in some beautiful New Zealand scenery, and the famous Raurimu Rail Spiral. See also: Train travel in New Zealand.
By plane
Hamilton International Airport hosts mostly domestic flights, with regular direct flights from:
Auckland - fares begin at $65 one way for a journey of 30 minutes
Wellington - fares start at $70 one way for a 1 hour journey
Christchurch - fares start at $135 one way direct for a 1 hr 40 minute journey Fares start at $70 if you stop in Wellington for half an hour
There are also regular flights to Sydney and Gold Coast in Australia
There are often limited specials available to/from Hamilton available on Grab-a-seat (http://www.grabaseat.co.nz/), Air New Zealand's website for its specials.
The airport is about 10 km 6 mi out of town, so allow plenty of time for airport transfers. A taxi or shuttle bus service is available but a rental car might be cheaper. Passengers who arrive on flights late in the evening on Fridays and Saturdays should arrange transport in advance as taxis can be scarce. Also, be aware that fog can close the airport on winter mornings.