I constantly get emails from students wanting to be my PhD student, or a PhD student in one of the research groups I am associated with. It has got to the point that I no longer have time to give an individual response to each expression of interest.
See the graduate research school's web site for information on pursuing a research degree at UNSW. I suggest you look through it as it has more up-to-date information than I can possibly provide here.
At minimum, here are some important points:
Unfortunately, international students in Australia are charged substantial tuition fees even for research degrees, whereas local students are not charged tuition fees.. See here for details.
This means that in practice, international student fees are covered by a government, university, or industry scholarships. For details of scholarships available, see here at UNSW and here at NICTA.
The award of scholarships is generally managed centrally via a competitive process. I cannot simply give you one, nor substantially influence the awarding of them, even if I am desperate to have you as my student. In order to be competitive for a scholarship, international postgraduate research students require an excellent academic record and evidence of strong research potential.
So if you have made it thus far, and believe you are still in the running, you need to convince me (or another member of one of the research groups I'm associated with) that you are truly interested in our area of research, have sufficient background, are capable and committed, and have enough of an outstanding academic record to have a chance of getting a scholarship. (You still need to convince me if you are a local student as well)
Note that I'm not trying to discourage you, I'm just pointing out the reality of becoming my research student.