1.  The cable modem will only support one computing device (computer or router).  If you have more than one computer or a PC and an XBox or a Wii, you must connect a router to the modem.  The router will let you support more than one device on the network.  You plug your devices into the router, not the modem.  Most routers come with four places to plug in devices.  If you use a wireless router, you can support many more than four computing devices on the network.

2.  Whenever you plug the Ethernet cable coming out of the cable modem to a different computing device (PC or router), you MUST unplug the modem from power for 20 - 30 seconds, plug in the device, then reapply power to the modem and let it come up.  Cable modems do not recognize new devices just by plugging them in.  This is different from a DSL modem, which automatically notices a new device and handles it accordingly.  So, if you unplug your desktop PC from the modem and plug in a laptop or another desktop, make sure you cycle power on the modem.

The first tip also applies to DSL and other modems, most of them only support connecting to one device, although I have seen some of the newer modems coming with built-in four-port routers.  Some of those are wireless, too.