First there is no way to play in online mode in retail games so forget about that and so far there is no way to bypass Xbox Live
What you can do though is play in LAN mode aka System Link x# online now with either
XBC [Xbox Connect] or xlink [Kailera] that run on your home computer
The above saves you having 2 or more TV's and Xbox's hooked up to a home network
Hooking everything up
You have 3 options that I can think of
1 a Crossover Cat5 cable hooked up to xbox and PC you are running one of the above software on
2 a Normal Cat5 cable hooked to xbox and router
3 a Normal Cat5 cable to Xbox and Network hub Cat5 cable to PC or router from Network hub
I will add installing and running much later when I have had more time to look at both options fully
At the moment I don't even think I have any Lan 2 or more player games on my xbox
When I get round to it my xbox is hooked up via Cat5 to my router and my laptop via WiFi thats option 2 for me then