Australia has a few big banks and many smaller, independent banks. You should compare banks to see which is best for you.
You can generally apply for an account online before taking the following to the bank in-person to finalise your account:
You may also be required to show your student visa and/or Confirmation of Enrolment (CoE) if you are opening a student account.
For more information, visit the NSW Government's budgeting and banking page.