Lets pretend everything you want to keep has been filed away in Documents. You drag and drop the Documents folder icon into the open folder representing the new external hard drive
http://www.wikihow.com/Copy-Files-to-an-External-Hard-Drive
http://techchannel.radioshack.com/transfer-files-internal-hard-drive-external-hard-drive-1453.html
I had an old Toshiba 80GB laptop. One night it made it down the steps before I did. The shattered case would shock me if I tried to use it, so I took the drive out and now use it as a storage drive via USB port.