Unless you installed some "client" or have a network share the only information you would leak are emails and sites you visit on their network.
Any information you send is pretty much open to all. This is well discussed and only those that are new to this area would claim there is a way to secure it all from everyone.
I use my Macbook Pro, I have OS X 10.8.5. I use it for union meetings and I'm worried that my employer's are scanning my info when I'm on their guest net. Is there encryption I could get? Would I need encryption or security or both? Or privacy software? Or a combination? I'd like to encrypt my files and protect my computer from others getting my information when I'm using the internet.