There's Home Sharing and Music Sharing and they are not identical:
iTunes: Setting up Home Sharing on your computer - http://support.apple.com/kb/HT4620
Music Sharing - http://support.apple.com/kb/HT2688
Home Sharing lets you copy iTunes purchases to another computer. Music Sharing lets you stream any music to another computer but not copy files. If these are not iTunes purchases you will have to manually copy them by either file sharing or copying onto another drive or media (e.g., flash drive).
Thanks for the reply. I didn't know there was a difference between music sharing and home sharing. Home sharing is what I'm trying to do.
My problem was that I was enabbling home sharing on each computer using different apple id's (in each iTunes). Once I logged into both iTunes with the same apple id, everything worked fine.