Firstly you will need to determine the appropriate structure for your Australian business. Most foreign-owned entities opt for a company structure – and when setting up a company in Australia, at least one director must be an Australian resident for tax purposes.
Once the structure is in place, you need to get your registrations in order. This means getting an Australian Business Number (ABN), investigating if you need to register for goods and services tax (GST) and also registering for a tax file number (TFN).
Read more details on setting up an Australian company here.