Cloudsurfer - You need to have an Australian Permenant Resident visa in order to apply for the ADF. To get this you either need to have close family who are Aus citizens or permanent residency visa holders themselves, or pass the skilled migration points test. You might get lucky if you were a refugee aswell..
I can't speak for the family route, but currently waiting in the skilled migration que for my visa so I can join the ADF I can tell you that it's a very long and expensive process, and in the end it only gets you to the first stage of recruitment! Be certain it's what you want to do.
For all the visa info you need check out
www.immi.gov.au, best of luck