The router should have MAC address filtering. That is, you should be
able to put the ethernet hardware addresses of the computers you don't
want accessing the Internet in the router configuration. That will allow
those computers to participate on the local network while not having
access to the WAN (Internet).

If your router doesn't have such filtering capabilities, suggest get a
better one. All the Linksys Cable/DSL routers I've set up have that
capability.

I've got a linksys router. This sounds good but I'm really uninformed (dumb)
here. Anybody know of a good step by step tutorial?

Karl