I will be starting my PhD at University of Melbourne this October and I have questions about the tutor position. Is this like a teaching assistant (TA) position in other university systems? What does the role of tutor entail? How are these jobs awarded, is it difficult to get one, and how much does it pay?
In Australia, a tutor is typically a casual academic staff member who runs "tutorial" sessions for classes of undergraduate students (typically 20-30 per one-hour class). Tutorial sessions form part of undergraduate coursework, however attendance may or may not be mandatory depending on the course and institution.
Tutorial sessions are normally used to review concepts covered in lectures, go through practice questions, or sometimes students use these classes as a place to collaborate on assignments.
Graduate students can apply to be a tutor for a particular course subject to availability (number of existing tutors, number of students enrolled, etc.). The best way to enquire would be to email course coordinators well in advance of the start of semester to enquire as to whether positions are available.
The pay rate for tutors varies widely, but it would normally be in the ball park of $40 - $100 per hour. The high section of the pay range (e.g. being paid $100 for a one hour session) normally assumes you are also spending time preparing material for the sessions.
Contact your PhD supervisor as they may be able to provide advice and contacts to get your foot in the door.
Side note: In addition to "tutors" in Australia we also have "laboratory demonstrators" who guide groups of 10-20 students through hands-on laboratories. If you are a STEM major you may be able to get a position as a laboratory demonstrator as well. These positions pay less than a tutor, however are more widely available.