How to get a tutoring position in Melbourne, Australia?
Wait, and you'll be contacted.

Start your PhD first. Once you're officially a student, when they're looking for tutors, they'll send a mass email to all PhD students. That's when you can sign up. These are internal emails - the positions are not advertised online, and you won't be able to find them via Google.

If you're still concerned, you can ask your prospective supervisor or the department receptionist.