Well I'm in first year now so have been through all of this. I'm at Usyd by the way.
What happens on the first day?
There's an orientation day where you can meet people who are going to be in your classes, ask questions etc. Then there's an enrolment day. You have to actually go in to uni and just write down the subjects you've chosen. Read the faculty of science handbook and speak to advisors beforehand though. I didn't do this and was a bit confused and unprepared for enrolment. It's fine though - you can change your subjects right up until 2 weeks into the first semester or something.
How does orientation etc work?
They'll mail you about when it's on. It's all fun and easy stuff - there are people you can ask all your questions about subjects. You just go to the uni to some room and chat to people about stuff.
Do you get to choose your own subjects?
Yep, it's great - you can pretty much choose anything in first year because all the subjects you're offered are pretty general. You just have to think about what levels of e.g. maths you're able to do. And you need to fill up 24 credit points per semester. You get two maths subjects, two science subjects (e.g. physics and chemistry) and then an elective subject. (I just did another science subject here and regretted it. SHould've chosen an arts-language one....ah well, i'm doing that for second year)
Do you choose your major straight up?
Nope. I still have only a vague idea what I'm majoring in. Think about what subject you enjoy, and have a look at the faculty of science handbook to see what kind of subjects you need to be doing to be able to major in it. Make sure you keep all options open as it's a bit annoying if you find that you can't major in it because haven't done the right subjects in first year. Biology majors in particular have alot of prerequisites you need to make sure you study in year 1/2 to be able to major in them.
How do you enrol to do courses that you need as a prerequisite for Masters?
The subjects you're offered are pretty 'general' in first year. It depends on specifically what you're after. But there will be advisors and everything there on the day so you shouldn't have any problems.