I did one at monash last year. This is how it works at monash, it's probably the same at melbourne so you can replace monash with melbourne in the following.
1. Apply for vac. scholarship at monash
2. They look at your marks, and if you're in the top 2 students in your uni, you get a offer from AMSI to sponsor/fund your project. Also you get to go to sydney for 2 days to present your work and network.
3. If you are not top 2 in your uni, you get a vac scholarship funded by monash. Don't get to go do sydney. Renumeration is the same though.
I don't think you apply directly to AMSI.
edit: Actually I think the process is more like this:
1. Apply for vac. scholarship at monash
2. If you are top X applicant (where X is the number of supervisors/projects available) they give you an offer and also automatically forward your info to AMSI.
3. If you are top 2 from your uni, AMSI will offer to fund your scholarship.
As you can see, it results in the same outcome, since they base everything off marks anyway.