Hey there Info Please, a very warm welcome to the world of MSO
I'm an international student and am from South Asia too. I only applied to UNSW last year because it exempts off-shore applicants from UMAT, which I couldn't appear because its not conducted in my country Bangladesh (and I was just too lazy to actually travel a long distance to sit a test!) so I can only fill you in about my experience of the application process at UNSW (and most unis I think follows the same basic procedure although there are differences for sure as meethu said). But the University does require int'l students to prove their English Language proficiency so I had to sit for IELTS (which isn't a big deal if you have command over English). I did GCE A-levels (which is the year 12 equivalent qualifications in the UK) and its pretty well recognised by the Aussie unis so I didn't have to explain them my qualification or have trouble filling in their 'optioned' online form. As far as I heard, the Go8 unis do not except HSC qualification (the Australian year 12 equivalent) of Bangladesh or Pakistan and require those students to complete a foundation year. If you do have any doubts, you can always e-mail them.
As beks291 already mentioned, you apply to the university directly. I applied online and it was quite easy. Its just a few steps of filling in information. Then you get a confirmation page which you need to print out and send it to the 'Direct Admissions Office' along with certified copies of your academic records. UNSW only accepts online payment by credit card, which is the most convinient way cause its instant, but I think other unis have the option of paying visa bank draft. Since you'll be applying to Medicine, you also need to fill in and send to the faculty the 'Medicine Application Form' which can be downloaded from the faculty's website. This form asks you some personal questions (like where & how you were brought up, your characteristics and the timeless question 'why you want to study medicine) and needs a comment from your institution's principal.
About 3-4 weeks after I applied, I got a mail to confirm a date for the interview. UNSW arranges telephone interviews for int'l students (I'm not sure about other unis) so I didn't need to travel. But it did get a little difficult cause we didn't get a good line and everything was hazy. The interview was quite personal and based on the information on my medicine application form. It lasted about 35 minutes.
2 weeks after my interview I got my offer letter and was totally excited and accepted it straight.
But you know what, I'm not studying at UNSW now and had to defer to 2010 because I was refused a freaking stupid visa!
Bangladesh, and I think Pakistan too, have been shifted to lower assesment levels (due to emerging radical Islamist militia maybe) so its quite difficult for us to get visas. Some say its also because of the recession, the DIAC has turned very unwelcoming. Whatever it is, I most unfortunately couldn't commence despite having secured a competitive offer, and they couldn't even show a proper reason for my visa refusal! Anyway, do not get deterred by that but just be aware to keep backup plans and try to lodge the visa application as early as possible.
Uh-oh, I drifted offtopic...sorry...coming back, this is pretty much it. Its quite easy and not complicated at all. As meethu mentioned, you should check each uni's website as they all have different procedures. And the websites are quite easy to navigate and contain most of the information you'll need its best if you visit them. And the uni ppl are quite friendly so don't hesitate to mail them if you do have any questions.
And about scholarships, I have to agree with Jono...hehe. Scholarships that cover a significant percentage of the tution (or even the full tution fees) are there at some unis (not UNSW though) for high-achievers, but none of them are for medical students! I scoured a lot of unis websites for scholarships for international students and all those that pay substantially have the following words written below "MBBS students/students of clinical programmes are not eligible"! So its pretty much self-finance if you want to study med at aus.
I kinda wrote a whole essay, please excuse me, posting long is one of my identifying characterstics...haha.
Hope it helps