Yep, very doable. My small home network consists of a cable modem which is connected to a router, which is connected to an ethernet card in each of my two computers. You can also use a switch instead of a router; it's cheaper but doesn't come with the built-in firewall the router has, plus I don't think you can use both connections at once with a switch (you can with a router). LinkSys products were recommended to me and that's what I used.
If your computers are far from each other you can set up a wireless network (more expensive), or just string a bunch of long cables, which is what I did. One of my computers is upstairs and the others is downstairs, so I drilled a little hole through the floor of my closet and into the unfinished part of the basement, where the router and cable modem live.