The easiest way to transfer files from an old computer to a new one is through 'my network places'. You will have to plug them into the internet. This will enable you to be able to share files between them. You can talk to a professional on networking to get more details.
You can pop out the hard drive and attach it to the new computer with a USB adaptor. You can even get a kit to make it into a portable drive. Either way, plug it into the new computer and copy the files.