Most student payments are administered by Services Australia (i.e. Centrelink). To find out which payment(s) you could be eligible for while you study, use their 'Payment and Services Finder'.
You can also check Services Australia's Guide to Payments.
The following payments are available for eligible students:
Youth Allowance - a payment for full-time students and Australian apprentices aged 16 to 24 years old.
Austudy - a payment for full-time students and Australian apprentices aged 25 years and older.
ABSTUDY - a living allowance payment plus a range of extra benefits for Aboriginal and Torres Strait Islander students and apprentices.
There are other payment and support for eligible students:
Tertiary Access Payment - a new payment to assist eligible students relocating from regional and remote areas to access higher-level tertiary studies.