What and how would I go about obtaining a licence for HAM radio in Australia?
Do the licencing regulations vary significantly from state to state?
From the Wireless Institute of Australia, to get one of the 3 license classes, you have to take an assessment. The assessment covers various amateur radio related topics, each level increasing the difficulty and depth of knowledge required to operate. They are set at the country level, thus there is no difference between states.
To figure out where to take the test, take a look at the WIA's list of assessors.
I've just sat my Foundation License on Sunday. It really depends what license you want to go for.
If you have no knowledge of radio (and to a lesser degree, electronics), you may want to start with the Foundation license. It's the easiest one to get. To get it, buy a copy of the Foundation License Manual and study it.
https://www.wia.org.au/licenses/foundation/foundationmanual/
Then when you reckon you know it all, sit a few of the practice theory exams:
http://www.wia.org.au/licenses/foundation/trialexam/
It may even be worth while to go to a local radio club to see if they can show you the practical side of things (how to set up a radio and configure it for transmitting etc).
When you feel confident enough, book in with one of the assessors that PearsonArtPhoto listed above. It'll be a two day course most likely. The first day and half is pretty much covering everything in the Manual. Then they'll sit you down, do the practical side of the test, then do the theory (25 question multiple choice, only need 70% to pass).
Congrats, you've got your Foundation license!
If you want to sit for your Standard or Advanced license, you will need to know a lot more about radios (and electronics as well, since you are allowed to build and modify equipment on a Standard or Advanced license). The two ways of doing it are
1 - Book in with a local club who are teaching these courses (not every radio club have people available to teach these two license grades). These courses normally go for 1 day a week for 6 months before they reckon you are good enough to sit the test.
2 - Go to Ron Bertrands radio school website. Order the Standard or Advanced license kit, do all the paper work, sit the trial exams and then book in for the exams. This option can be done at your own pace.
The only problem with going straight for your Standard or Advanced license is you will still need to sit the practical part of the exam. Still may be a good idea to have a talk with a local radio club to see if you can sit down with a tutor (if they have one available) to show you the proper way of doing things.
If you sit the Foundation license exam and practical first, you will never have to do the practical again afterwards even if you upgrade to the Standard or Advanced license in the future.
I have a friend of mine who designs circuit boards for a living. He's going straight for his Advanced license but still came down to my radio club to get a hands on for the practical side of things.
Out of curiosity, which state are you in? I'm in NSW, so I can give you further details if you require it.
EDIT - Forgot to add, the licenses don't vary from state to state. It is an Australian wide certification. If you move states permanently, you will have to change callsigns as they are dependant on state (VK2 callsigns are NSW, VK1 is ACT, VK0 is Antartica!)