Having only one drive pretty much negates the purpose of doing a backup. If your hard drive dies, you lose both the original data and the backup.
You will need some type of secondary device to perform a backup, whether the backup is to contain just your data files or the entire hard drive. If you want to backup just the data files, then depending on the number and size of the files, you could use a floppy, USB flash drive, CD drive, hard drive, or online backup. To make a clone of the entire hard drive, you will usually need another hard drive, either internal or external. There are some good deals now on USB/firewire external hard drives.