If you do use an unlocked wireless internet connection can they see what websites and other activities?

you do while on the computer? Let's say you use a public wifi connection or use someone else's connection (while illegal) can the host see what you do while on the connection? Is it possible that if you do use someone's unlocked account that they can find you? I mean I've heard people say they cant and blah blah blah but I don't want to go to jail while just checking out a few websites. What penalties are associated with using someone else's connection? Is it like taking the tag off your mattress? I say this becasue is it something that many people do and it is just commonplace?