Martin, you need a network hub and both your computers have to have network cards in them (if not then you have to buy them). Then all you have to do is follow the instructions that come with the network hub and you're all set to go. You can also buy a network starter kit which comes with a network hub and either 1 or 2 network cards.
Your other option is to take the hard drive out of the old computer and attach it to the new computer. If you're not computer savvy then you should get someone to help you do this or you can bring it into a computer shop and they can do it for you for a fee.
I would personally go with the second option (attach old hard drive to new computer).