Hi,
What steps must I take in order to set up my own business in tutoring primary school age students?

Hi Narelle,
Presumably you are doing this tutoring in your personal name as a sole trader.
If that's the case then you will need to have an ABN (Australian Business Number). This can we obtained from the ATO website.
You can then give your students tax invoices.
Presumably your income will be under $75,000 then you will not have to register for GST.
All the best with the tutoring.
Kind regards.