Not much, it's a question of quality over quantity. If you've been paying attention in class over the last 5 years then a lot of the HSC work will be familiar to you, either in skills (research/analysis in history, maths ability in maths) or in content (a lot of HSC science is yr 7-10 stuff). If you haven't then you need to make sure that you learn everything the first time, so if you don't get it in class go home and revise it until you really understand it. You can't afford to fall behind, and that goes with assignments too.
As long as you stay on top of things the HSC will be easy, if you understand the general concepts then it will be really easy to learn the specifics when you need them. The reason why so many people bomb out is either because they don't wholly grasp the stuff they need to know and they think they do, or because they don't wholly grasp the stuff they need to know and leave it until the exams, or because they don't wholly grasp the stuff they need to know and don't bother studying at all, I think you see the pattern.
So in answer to your question, if there weren't any major assessment tasks I spent anywhere between 0 and 2 hours a night working, in the weeks leading up to exams such as half yearlies then probably about 2-3, in the weeks before the trials then about 4+ hours per night. That said you just need to adjust your schedule to make sure that you know everything that you've been taught up until that point and that you're not burning yourself out, remember that the weekends are great for just spending a couple of hours going over the week's work, and that teachers give homework for a reason, it's usually a good idea to do it.
Anyway that's from a maths/science perspective, it would probably be different for an english/history student.
[Edit] And when I say 0-2 hours of work I mean 0-2 hours of work, not 1.5 hours of browsing forums, colour coding your notes, texting someone or anything like that. One of the biggest obstacles facing any yr 12 student is procrastination, really if something is distracting you and preventing your from working turn it off, lock it away, destroy it if necessary, if you find you're having trouble researching on the internet ask your parents to supervise you so you don't go on MSN or something. It may sound embarrassing and less fun, but if you want a 99+ UAI it's the way it's got to be
