By plane
Invercargill Airport is about 3 km from Invercargill's Central Business District. It is served by Air New Zealand (http://www.airnewzealand....) with flights from Christchurch and Wellington. A flight from Christchurch to Invercargill takes about an hour in a turboprop aircraft. On a clear day the flight is spectacular, with the Southern Alps to the west of the flight path. If flying south to Invercargill be sure to request a window seat on the right or starboard side of the aircraft request port or left if flying out to Christchurch. Mount Cook, which is visible about half way through the flight, is merely the biggest of the many massive peaks of the Southern Alps. A direct flight from Wellington takes around 2 and a half hours.
By bus
InterCity Coachlines (http://www.intercity.co.nz/) is New Zealand's national coach company and operates over 150 services to more than 600 destinations nationwide. They operate daily services from Dunedin to Invercargill and Christchurch as well as to Queenstown and other places in the southern lakes district. The low cost bus option is nakedbus.com (http://nakedbus.com/) with competitive prices.
Knight Rider (http://www.knightrider.co.nz/) is six times per week option from Christchurch and Dunedin. It arrives in Invercargill at 3.00 AM.
Catch-a-Bus (http://www.catchabussouth...) provides service to Dunedin six times a week. This service will pick you up at your door.
By car
Invercargill is the main focal point of numbered highways in Southland.
Heading south from Dunedin you can follow State Highway 1 to Invercargill, with a travelling time of about two-and-a-half hours. Alternatively you can leave SH 1 at Balclutha and follow the Southern Scenic Route (http://www.southernscenic...), often called SH 92, through the Catlins. While only a half hour longer to drive, allow a day for this trip at there's heaps of natural attractions to see.
Invercargill is about two-and-a-half hours south of Queenstown via SH 6.
In addition, following SH 99 through Riverton you can reach Te Anau in about two-and-a-quarter hours.