If you already have a router, then all you need to do if have both computers plugged into it and it should assign I.P.'s automatically. If you do not have a router, the cheapest thing to do, is to buy (or make) a cross over cable. They are different than regular network cables.
More than likely, you are running a 32 bit OS.
Instead of writing how to assign an I.P. address, here's a link..
http://hubpages.com/hub/How-to-Configure-IP-Address-on-Windows-XP
If you go the cross over route, you only need to worry about assigning an I.P. address to each computer, do not worry about DNS or Gateways.