you cant network 2 computers with a standard cable. You need to either use a switch, or a hub, or a router, Or you have to get a special "Crossover Cable".
once you have the 2 computers on the network you have to share the hard drive or folder of the old computer so that you can copy stuff from it on the new computer. Sharing a drive or folder is a little different depending on the version of Windows you the old computer is using.
The procedure is easy but there are a lot of steps involved. You would be best suited searching for a guide that has already been written.
By installing Windows Easy transfer you can save all your data in standard locations but you can also select custom folders and directories through the use of LAN or USB port.
Windows Easy Transfer is very easy to use as I myself used it before but you need to find the Windows Easy Transfer compatible to your situation. For my situation I've used the Windows Easy Transfer for Windows XP to Windows 7.
I found this site that includes the listing of the other versions.
I have never had a problem connecting my laptop and desktop directly with a standard ethernet cable. I do it a lot if I have to transfer large files, because its faster than running it through my router/switch. I think it depends on your network adapter though, this is straight from microsofts website:
"Before buying a crossover cable, check your network adapter. Some newer network adapters automatically "cross over" when they detect that they are connected directly to another network adapter using a regular Ethernet cable."