There are several steps and gotcha's. Don't try and do things yourself to save money. It will end up costing you more.
1. Register yourself as a specialist with AHPRA
2. Find a billing service. This can be a stand alone billing service or an anaesthetic group. Do not try to do your own billing. Any costs saved in avoiding a 5% commission are outweighed by the mistakes you will make, and time spent, by doing it yourself. Make sure they offer an IFC (informed financial consent) service. IFC is a requirement for health funds to rebate at above the MBS rate.
3. Register yourself with all the health funds through your billing service. Do not submit the paperwork to the funds yourself, let the billing service do this.
HCF and BUPA - Decide whether you want to register as a "Gap" or "No Gap" provider. This must be explicitly stated on the form, even if there is no box for it. Most anaesthetists register as a "Gap" provider.
4. Apply for accreditation at private hospitals in advance. For small hospitals this process is quick, but larger hospitals this can take a while.
Do this stategically. Many hospitals are part of a network (eg Healthscope, Ramsay). Apply at one hospital in each network. Once you are accredited at one hospital in the network, it is quick to get accreditation at the others as they can get accreditation documents from the other hospital in the network.
5. Decide what you are going to do about your NIB patients (see http://faq.patientloops.com/22/what-does-nibs-new-terms-agreement-mean-for-patients-myself) If you "No Gap/Medigap" an NIB patient you are implicitly agreeing allow NIB to publish your gap statistics on their website, amongst other things.
6. Get a business card. Include your name, mobile, and email address. Give this to every surgeon you work with that you would like to work with again. Say "Here are my contact details if you need anything".