For instance, I have an open ticket for one of our offices on the east coast. They have two model homes with an internet connection, and they want to set up some extra computers. The desk side technician went out and bought some network switches to split the internet connection up. He plugged the cable modem into the switch then two computers. One computer had access, the other couldn't pull a n IP address from DHCP, so he called me. After him explaining this to me I wanted to reach through the phone and ring his neck!
When you order your high speed, broadband internet connection you are essentially renting an IP address from your internet service provider. If you have a T1 connection, you might have three or four IP addresses to use. This office was a model home in a residential area, so they only have a regular old cable modem. with that cable modem only comes one IP address from the cable company. In order for you to share your internet with this type of setup you need something that can perform Network Address Translation (NAT) to change that one Public IP address into multiple Private IP addresses. You then need to have something on your new private network to automatically assign IP addresses to each machine (or you have to manually set static addresses, trust me, it is easier to have it automatically set).
All of this can be performed with a simple home network router. The router will take that one IP address from the ISP, translate it into a private address, the router will then split that traffic between all of the hosts as well has assign each host an IP address of their own. This sort of setup is very common in SOHO networks, and I am thoroughly surprised that the desk side technicians couldn't figure that out!
So the moral of the story: If you want to share your internet connection with more than one computers at home... GET A ROUTER!!!