1. External (the easiest but usually most costly)
-Get an external enclosure for your hard drive and connect it to the new computer via USB, firewire or eSata
-transfer the data over. You'll probably get a sustained 15-25mb/s over USB 2.0
2. Ethernet (usually less costly because you probably have the equipment already)
-connect both computers to your home network and transfer data via the network. Max transfer rate assuming it's not gigabit: 10mb/s
-You could also just grab one ethernet cable and connect the computers to eachother via a peer-to-peer network.
-You'll need to share a folder on your new computer to put the files into and use your old computer to transfer the data to it in "my network places"
-Install the hard drive into your new computer as a slave. Turn on your new computer. You now have full access to the drive and can transfer over all the data you want.
-Maximum transfer rate: only limited by the speed of the hard drives.
Too add to what enzo said once you figure out you configuration there are a few programs that will make exact copies of the hard drive I suggest Acronis True Image its really easy to understand interface and will guide you thru the whole process.