Time Machine is a built-in backup system in OS X that backs up all of your files to an external hard drive so that you can restore them later or see how they looked in the past. It requires an external hard drive of some kind, whether it be an attached USB drive, a network storage drive, or an Apple Time Capsule.
With many households today having several Apple computers, it is likely that there will be a few Macs that need to be backed up to the same storage device, often for multiple users. Personally, I use a separate USB drive attached to my iMac for the most efficient, easiest backup solution, but our three MacBooks are backed up to a single Time Capsule.
The easiest method of setting up access to the shared disk on a Time Capsule is to use the base system password, but that password is used to reconfigure your Time Capsule, so that’s a really bad idea. Conversely, the most-recommended option is to specify a disk password. This assigns a separate password for use with Time Machine which cannot be used to reconfigure the Time Capsule and therefore does not compromise its security.
The final (and, in my opinion, best) option available is to set up different user accounts, each with its own name and password. This is the most secure but least used option, mainly because there’s a widely held misconception that it is extremely difficult to perform maintenance on the Time Capsule because each account user can only see their own space on the disk. Time Capsules frequently run out of disk space, and Time Machine will delete the oldest backups to make room — but only for the Mac it’s running on, and no others!
The Secret Solution
Apple has a secret, undocumented solution! There is one built-in user that can access all of the user folders. Browse to your Time Capsule using Finder. Click the “Connect As…” button. Enter “admin” as the Name, and the Time Capsule’s Base Station password in the Password field. This is a pseudo-root user that has access to all users’ folders and data.
Exactly how to use that user to perform maintenance and analyze usage is a topic for another time.