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The drive may need to be reformatted. You do this via Disk Utility - see below.
If you want the drive to be a bootable one, i.e. you can start up your computer from it, then you need to use a Firewire connection. Does your drive have FW or is it USB?
If you have FW, then the first thing to do is partition the drive in Disk Utility (Utilities folder). When open, click on your HD, then click on the Partition panel. There, you can name the HD, and select its format - the format would be "Mac OS Extended". You can set up one or more partitions depending how you want to use the drive. If it is just for a backup of the computer, then one partition would suffice. If you want to save files
For the backup process I recommend
SuperDuper. Very easy to use. The initial backup takes about 1 to 2 hours. Subsequent backups (referred to as "incremental backups" take 5 to 10 minutes, copying or deleting only those files that have changed since the previous backup. This way, you have a complete backup of your system on hand.
Other than data security, this backup can be used as an effective backup just in case an upgrade to your system fails or has problems. For example, prior to upgrading the OS, you update your drive to the most current state of your computer. Then you upgrade. If there is a problem with the upgrade, you simply start up from the External drive, then copy back via SuperDuper the drive's contents to your computer (takes about 5 minutes). This restores your computer to its state prior to the upgrade. This can be a huge time saving tool.
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