I'd like to set up Amarok so that several users on several different computers can use it. Ideally, one computer would serve the music to others, but I could live with different independent versions of Amarok that are all accessing the same music files.

How hard is this? Is it even possible? I'm relatively new to Amarok but have been impressed with what I've seen so far!

Thank you!

You can use NFS or other local network sharing protocols (like SMB/Samba, etc).
Simply host them all on one system then mount it up into the system on the other computers.

You could configure the machines to all use the same MySQL database, but one machine cannot be used to control another with Amarok as far as I am aware.