IP Addresses:

Everything that communicates on a network with TCP/IP ( the default for everything ) needs an IP address. To setup your network so it can work with Kai, you need to understand a few basics.
First is range. An ip address must be in the same range to enable a device to communicate with another device. ( There are other ways, but i'm keeping this basic. )
For example. 192.168.1.1 is different then 192.168.0.1.
In order for two devices to “talk” they need to be in the same range. This would be an example of two ip addresses in a range.
192.168.1.1 and 192.168.1.2, notice the first three digits are the same. This is crucial. I won't bother explaining the significance of the first three digits.

Subnets:

Subnets are used to either break down large networks, or expand smaller ones. Since this isn't a topic of concern, you want to use the default subnet for the ip address you've chosen.
Which would be 255.255.255.0

Gateways:

Gateways are the devices your computer looks to in order to communicate with the internet. If your computers hooked up to a router, then the gateway is the ip address of the router. If its hooked directly into the modem, use DHCP to grab all the settings for you. If its an Xbox trying to communicate with the internet ( Kai ) then you want it to be either the router or your computer.
When you use your Xbox with a cross-over cable to your computer, you want the gateway to be your computer. The data is being transferred from your Xbox, to your PC, and then to the internet.
If your Xbox is hooked up to a router, then you want it set to DHCP and grab the settings for you.
Using the knowledge from the last section, if your Xbox is hooked up to your PC via a Cross-over cable. This is how your Xbox should be configured if your computers IP address is 192.168.1.1

• Xbox IP: 192.168.1.2
• Subnet: 255.255.255.0
• Gateway: 192.168.1.1 ( Computers IP )

Routers and Switches/Hubs:

A router is a NAT. It turns one IP address into many, meaning all your devices that connect to the router can talk to the internet using different IP addresses that in the end are turned into one. Most ( if not all ) routers have DHCP. DHCP is a server that assigns IP addresses according to a predefined range. It allows for “Plug and Play” operations with network devices, since most of the hard-work is done behind the scenes.
Routers also tend to have built in firewalls, port-forwarding and other features.
Port-forwarding on a router is sometimes needed because the router cannot figure out where to send the data its receiving. Unlike a switch or hub which broadcasts the data to all the devices, a router sends it to one device because it has a routing table.
What this means to the end user is that if you cannot get traffic to your Xbox, you need to tell the router where to send the packets. This is port-forwarding. However instead of telling it to send data to the Xbox ( For Xbox live ) you want it sending it to the PC because Kai is ran and processed through the PC.
Switches and Hubs however are different beasts. Switches forward data based on mac addresses, while hubs only allow one device to send data at a time.
The reason port-forwarding isn't really needed with hubs is because it broadcasts the data on every imaginable port to every device on the network. Eventually it'll get to the right one. Its inefficient, and should be avoided. Collisions are frequent, and since Kai uses UDP packets, the transmitted data won't get resent.
If you want a simple network, use a switch. If you want an easy network with a bit of headache use a router. If you want a slow gaming experience, use a hub.

Internet Connection Sharing:

This allows a network connection to be shared to other devices. It is meant to allow multiple computers to use another computers internet connection. However for use of cross-over cables to the xbox, it will allow the xbox to use your internet connection to talk to kai.
This is needed for almost any pc to xbox with a cross-over configuration.
Thats networking in a nutshell, i'll add more as I think of it. Use this as a reference to understand the concepts of networking, and that way you aren't just doing a set of instructions, you're understanding the steps and what they do. Thus you'll be able to help yourself if you think about the problem a little bit.