You have two options, you could have one computer act as a dedicated server which would allow the other computers to connect to it so they can play, but the dedicated server cannot be used for playing. Your other option would be to host a game (non-dedicated) from one of the computers that the others could join which would allow all the computers to play but playing from the host computer could be taxing on all machines if its not beefed up enough to where it can host and play at the same time. In any of the cases each machine would have to have a copy of Quake 3 installed in order to play.
Let me know if this helps or if you need more detail.