The best place to start is the VTAC website. That's where you apply for uni. You can apply whilst waiting to sit the STAT test as long as you have the results before decisions are made. Their website is here delta.vtac.edu.au - Home and it has details of the STAT test under "Admission tests".

The test itself is an aptitude test with maths and comprehension components. It is for people who haven't recently studied and is for most courses (exluding law and medicine), but if you don't want to sit it then you can apply to the university directly to study one or two individual units which would demonstrate to the uni that you are able to study at degree level.