Cheapest way to do it is thus (I know, I've just done it).
Purchase two wireless network PCi cards. Install one in each PC. Configure 'Internet Connection Sharing' on each PC (a quick google on the subject will help, its pretty simple) and you are up and away!
Only catch compared to the router solution is that PC no1 will have to be booted up for PC no 2 to be able to access the internet.
(PM me if you wish to go down the xbox route - this was the only problem I had and the solution eventually was surprisingly simple).