depend on what kind of priviledge you talking about,
do they have a user account, limited user account, power user account, internet access, email access, is there a wireless router in the network, how much they know about the school network, do they know anyone that has access to the main computers, is any of them friend with someone that has remote connection access, does anyone of them do any work at the office that has the main computers, etc... if they are hackers there is many ways they can do it.
starting from using some social engeniering to get the information they need, to using some of the tools like: key loguers, snifferes, brute force, knoppix and others.
this is hard to think about with out a physical view of the network setup, configuration settings and/ or location of the computers in the campus, etc...
however, just be carefull when you configure your router and firewall, may be change the remote connection port, make strong passwords, and keep track of who has access to this or that, etc.. there are many things that can prevent them from getting access, how ever remember that there is no such thing as a totaly secure network and kids this days they know the way around this kind of things!
at least the more difficult you make it for them, the longer will take them to break in and they don't like that because that means that there is more chances for them to get pinch!
i hope this could help you in some way!!
