There is a special student visa that you need to apply for. It basically says that you are a resident of Hong Kong for so long (either a semester or year depending on how long you study here) and that you can reside in the SAR. It is also really good because if you travel a lot like I am doing, then you get to go into the Hong Kong Residents line in Immigration instead of waiting in the really long lines for Visitors
I think that you must be a full time student to get the student visa, but don't quote me on that.
I know that to get a student visa, you have to have a original letter signed by the institution that you are studying at saying that they are enrolling you for the semester/year. Also, you need proof of financial stability as well as copies of your passport and transcript.
I'm studying at the Hong Kong University of Science and Technology right now and they actually intervene on behalf of their study abroad kids to help get the visas processed and everything taken care of. It was fairly simple because my school helped, but I have heard that it can take some time to get a student visa processed if you do it by yourself.
HTH,
c
