There are not many ways in which a person is not able to get to the Northern Territory, but unless there is lots of rain, by boat is a very unlikely way of getting to Alice Springs. The easiest and fastest way is by flying, Alice Springs has a modern airport, it's even air conditioned.
Regular flights are available from most major cities in Australia.
I understand that the flight from Adelaide to Alice is one of the cheaper options, or from Darwin to Alice. Refer to Location for information on distances from major centres. Rail Rail Travel to Alice Springs is only available from Adelaide directly, known as the Ghan , it is one of the great train trips in the world. The Ghan also connects with trains from Eastern States, or Perth in Adelaide. If you have a car it can be transported at the same time on the train.