Depends on the game. There is a specific LAN setting for some.
If not, you're probably going to have to put up a server just like if you played online.
If you know how to do that you should be able to connect to it just like you would to any other server.
Oh and you DON'T need an internet connection.
If this doesn't help you, you had better tell us the name of the game(s). I'm not much of an expert on setting up servers OR LAN gaming, but I've done both a couple of times, so maybe I can help if I know what game we're talking about.