You'll need to plug it into another computer, either internally via SATA/IDE (depends on the drive) or externally using an enclosure (available many places online). Once you plug it in and reboot the computer it should appear as an additional hard drive that you can then backup/copy-paste. If you don't have access to an easily opened desktop I would probably go the enclosure route. Plus when you're done you can wipe the old drive and use it as an extra external hard drive!