Any computer that connects to a network wirelessly needs special Wi-Fi hardware. Most recent notebooks have it built in. If yours doesn't, you can get a USB or PC Card wireless adapter for cheap. The buzzwords nowadays are Wi-Fi, 802.11g (or the older and a bit slower 802.11b), and, in the Apple world, AirPort.
Once your computers have what they need, you'll need to get what's sometimes called a "gateway," but is most often known as a router. Some are purely wired, and some are mostly wireless, but we'd recommend a combo that's known as a 4-port wireless router. Each of those four ports has that fat ethernet (RJ-45) connector, so you can connect up to four devices directly--a couple of computers, maybe a printer and a hard drive. The wireless part can talk with even more Wi-Fi devices. Plug the router into your cable modem and plug your computer into the router.
And for a moment, now, things get complicated. If you're lucky, the router will come with great instructions to take you the rest of the way. And, again if you're lucky, all your computers run either Windows XP or a recent version of Mac OS. (If not, please seriously ask yourself if this is a must-do project for your home. There be dragons.) Windows XP comes with a couple of setup wizards that can help you configure your network. With Macs, it's a matter of a few clicks. And it's possible to have a network with both Macs and Windows PCs on it.
When all this works, it's great. But when it comes to networking, it's easy to run into trouble, and it's tricky to figure out what's wrong. It's probably best to check first whether every machine on the network can get to the Web. Setting up file and printer sharing between machines can be trickier. And there's plenty to run amok: Is it the hardware or the software that's causing problems? Is it the router, the wireless signal, or the firewall? Lots of things can go wrong. So if you can, try to get somebody who knows this stuff to help you set things up.
So what's all this going to cost you? Let's assume your desktop machine already has an ethernet port. A 4-port wireless router will set you back maybe $60. If your notebook needs that adapter Steve and Angela mentioned, a USB adapter goes for less than $40. That leaves an ethernet cable for any machine that's near the router, and a 10-footer will cost you maybe $10. Shopping around can score excellent bargains on this project--and once you've got a home net working, you'll wonder how you ever got along without it.