How do I apply for a master’s in the USA if I am an Australian citizen who studied in India until my bachelor’s?
You should follow exactly the same rules as any international student would.
The complete application process would more or less remain same. However, every university has its website where it publishes information regarding international students. Some universities would explicitly share information pertaining to application process based on the country that you hail from and some wouldn't.
If you are skeptical of the application process, you could anyway write to the international student’s office and seek assistance pertaining the same.
Nevertheless, your Visa process is surely going to be different than that of any Indian student applying. Again, even for that, you will have to visit website Apply for a U.S. Visa (This link is for exclusively for Australian citizens).
Hope this helped. 🙂