I take it these machines are not physically close to each other? If so, your cheapest option is to probably buy 2 Homepna cards (assuming you have phone jacks near each machine on the same phoneline). See
http://www.homepna.org/ for info. Buy the cards direct from
Netgear for $20 to $30 apiece, or search Ebay for good deals. Make sure you get Homepna 2.0 cards, rather than 1.0 (2.0 is 10 times faster.)
The cheapest setup requires the use of an always on machine that will act as the internet server to the other. If you want a router, Homepna becomes more expensive, because you need to buy a separate hpna/ethernet bridge. Some routers, such as the 2wire homeportal, have built-in hpna support, and you can get these on ebay for $110 or less.
Your other options are homeplug (powerline) and wireless. Both have their advantages, but if cheap as possible is the goal, I don't think you can beat Homepna.
See also the
AN Networking FAQs.
Write back if you want more info. Good luck. RW