How to restore files from another backup set with OS X Time Machine

I needed to find a file from a retired OS X machine. I still had the Time Machine backups, but by default, Time Machine only looks at the current machine's backup set.

The solution is simple--just a matter of finding the where the right option is hidden. Hold down the Option (alt) key, and click on the Time Machine icon in the menu bar, or click and hold on the Time Machine option in the dock. You'll get a "Browse other Time Machine disks..." option. Select that, and then proceed normally.