The previous advice is correct a router is the answer.
To avoid cables you could go for a wireless router, you might need to purchase wireless adaptors but its a neater solution.
If you go for a wireless router then be sure to setup the encryption, and there is usually an option in the router setup to spoof the ip address of the computer. You must set this to allow the router to share the internet connection.
Any problems/questions post a reply and I'll try to help.
Andy, April 2008
Assuming that you use some kind of broadband service (ADSL, Cable) via a suitable modem the answer is yes but .....
You connect one as usual, connect the other one to it via an Ethernet cross-over cable and then set up Connection Sharing in Widows.
The but is this can be difficult to do if you are novice and the computer connected to the modem has to be switch on for the other to be able to connect to the internet.
My advice is to buy a router. It will be much quicker and easier to set up and they can be got very cheaply these days.
