I did this, however, with an xbox 360. Offhand, I can't remember what I did. But there was a tab in network properties somewhere that I found a checkbox that literally said "share this connection" and that was it.
My reasoning behind it was simply that my router was maxed out and I wanted the 360 online, so I put two PCI LAN cards in a desktop nearby and ran it to that and it worked.
However, a router will still be the best way to go. Yeah, it costs a couple bucks... But you gain a ton of functionality.