...Does the old one have an Ethernet port? Nevermind that question, I should have inferred tha to begin with form your opening post. I must confess, networking is the bane of my computer experience. Normally I am very good with them. But when it comes to networks. I get angry. I scream. I curse like a sailor.
What you would need to do is set up an ad-hoc network if you are connecting the two without a router, or a normal network if using a router. Either way, make sure to use a static IP address for both computers!