How do I setup my PC to be a server on my LAN only?

Quite easy

Just use the "Create"-Button in the main menue, give your server a name and make the settings of your choice. Start the match. The other PC's should find your server then on the "join"-Serverlist.

Well that will create a listen server, meaning your player is always connected. Not sure what you want to do with your Nexuiz server but maybe a dedicated server is more like what you want. That thing just runs a server and others can connect.
I wrote some stuff about how to setup a dedcated server in the [/b]Nexuiz - General Discussion[/b] forum, its called Sticky: server setup guide : http://forums.alientrap.local/viewtopic.php?t=18