To learn about UNIX, see UNIX 101: Basic UNIX . From the computer labs at UIC, you have access to your account on icarus. A nice way to access icarus is to run X Windows via Exceed.
If you work at home on a windows machine, you can run the gnu tools with the Cygwin tools.
Another way to get the gnu C compiler is to install the Minimalist GNU for Windows.
You can download lcc-win from http://www.cs.virginia.edu/~lcc-win32/ which is a Win32 C compiler complete with integrated environment.