Yes you can buy a Network card for £10 eg. Netgear FA311 @£7 from Amazon, easy to install.
I'm assuming your on adsl (BT,Tiscali,Wanadoo etc) and not cable (NTL,telewest).
a)El Cheapo, if you've no cash to spend, once you have the 2 PCs connected with a crossover cable, you enable Internet Connection Sharing (ICS) on the computer connected to the internet. Problem is it has to be on for the other PC to get Internet access.
b)Prefered Wired option using ADSL router such as Netgear DG834 and patch cables
c)Even more prefered and not much more is to buy the wireless router version and you can always go wireless anytime in the future for not much more £. Netgear DG834G £60 or Belkin F5D7632UK. Patch cables for wired connections.