I think that the easiest way to backup a home computer is using the operating system's built-in backup tool and an external hard drive. The Mac's Time Machine app is really easy to use, but Windows' backup/restore that you access via the control panel isn't too difficult either.
You can also backup to DVDs, but that's an awkward method now that hard drives are so large. Personally I also do frequent backups of my most important files to a USB thumb drive, but those have limited space, too. If you want to back up everything - photos, videos, music, etc., an external hard drive is a better option.