By bus
Greyhound (http://www.greyhound.com.au)] ply the route to Alice Springs from the north and the south.
By train
The Ghan is a private tourist train covering the vast distance from Adelaide to Darwin stopping in Alice. Expect to pay a premium over the airfare, even for a sitting seat. You can put your car on the train.
By car
Alice Springs is 17 hours drive from Darwin, and 18 hours drive from Adelaide. The Stuart Highway from Adelaide is well-maintained and goes right through Coober Pedy, an underground town famous also for being the opal capital of the world and therefore well worth stopping off for a visit on the way. It continues through Tennant Creek and Katherine all the way up to Darwin.
If you are driving on the main sealed routes from other Australian Capital cities, you will likely not be driving on remote roads, and provided you do not take side trips, there will likely be passing traffic. It is worthwhile reading the safety tips for Driving in Australia and always carrying water and ensuring you know the location and opening hours of your fuel and food stops.
Read the rental car conditions carefully. Rental cars in Alice Springs may not offer unlimited free kilometres. Rental cars hired outside of the Northern Territory may not be able to be driven into it. Driving after dark outside of the city limits may be prohibited. Rental companies in AC do not offer hand-controls for the handicapped.
The official visitor information centre has access to unlimited kilometre rates, so it's worth getting in touch with them if you are going to clock up the Kms on the car! (http://www.centralaustral...)