Ok, here are the steps:
The computer that's going to run the server-have it start the server, and take note of the IP address of that computer. Have every computer on which someone will be playing open Gens, and then Netplay in the File menu. When the Kaillera client opens, have everyone put a name into the box in the lower left, set the connection type in the lower-right to LAN (it'll help the connection), click the Enter IP button at the bottom, type in the IP address of the computer that's running the server, and click Connect. Once everyone's on the server, have one of them do Create New Game in the Kaillera window, have everyone else join that game, and then have the first player click Start game, and everyone's game will begin.
Note that the game is never started until everyone connects to Kaillera, one person creates the game on the Kaillera server, and everyone joins.