I study at a college where most social networking sites are banned(Including this one) and if someone is found using them somehow is heavily fined.I just want to know what all can the network admin find out
Depends on the way you use SSH. If you just do it the usual way of using the
-D option to provide a SOCKS server and use this as the proxy at the browser, they will not see that you are accessing these sites but they might deduce the use of such sites from tracking DNS queries.
ssh -D provides only a SOCKS4 server and for SOCKS4 the resolving of host names to IP addresses must be done outside the SOCKS4 tunnel, because SOCKS4 can only handle connections to IP addresses.
Edit: thanks to dr jimbob for pointing out, that SOCKS5 is available in ssh since 2003, but that have to make sure to use this version. With Firefox you have to explicitly choose the SOCKS version and you need also to explicitly enable RemoteDNS to make the DNS lookups through the SOCKS5 proxy.