How do you access another user's Time Machine backup?

Is the other backup drive another Time Capsule or another network drive.....or.....is the other backup drive a USB or FireWire drive?

If it is another USB or FireWire drive, there is really no need to use Time Machine at all here. Simply let the drive mount on your Mac's desktop and the open the drive.

Backups are in a folder named Backups.backupdb

Open the Backups.backupdb folder and the name of the Mac will appear as another folder

Open that folder to reveal list of folders with different backup dates

Select the date/folder that you want and open it up to reveal Macintosh HD, or whatever the user has named the drive

Keep drilling down through folder levels to find the files that you want

If you are asked for a password early in the process, the user has likely encrypted his backups, and you will need that password to proceed

The same process can be followed even if the backups are on another Time Capsule. Time Machine does not need to be opened.

Open the drive on the Time Capsule.....named "Data".....unless it has been renamed and locate the sparsebundle file for the Mac.

Open the sparsebundle file

That will mount a drive called Time Machine Backups on the desktop

Open Time Machine Backups

Open the Backups.backupdb folder and proceed as above

If you are asked for a password, the user has likely encrypted his backups.

Before going into Time Machine, open a Finder window and choose "Computer" from the Finder's Go menu. (That's the key to being able to browse another computer's backup drive.)

Then hold the option key and choose "Browse Other Backup Disks".

Hope this helps.

I should clarify: Being in the "Computer" window is the key to being able to browse a different computer's backup disk. You can also get there once within Time Machine, but it's easier to get there beforehand via the Go menu in the Finder.

After clicking on OPTION, WHERE do I see this option ... Browse Other Backup Disks?

I am on Sierra OS.

It would be the Time Machine icon on the macOS menu bar. So while holding down the Option key, click on the icon to reveal the “Browse Other Backup Disks” option in the drop-down menu.