Apple’s included Time Machine backup technology in macOS is a convenient and rather thorough way to make full-system backups of your Mac. It works by using multi-linked files on the backup drive to mirror unchanged data from a prior backup instance to a new one so both instances share the same data on disk. It then only copies changed data since the last backup, to the new backup instance. This approach allows Time Machine to create many snapshots of the entire system without any data redundancy on disk.
Whether it uses a disk image on a Time Capsule, or an external drive, Time Machine uses the raw HFS+ (Mac OS Extended) filesystem as a storage medium, which means that in addition to the Time Machine interface, you can use other means to access the Time Machine backup data.
The Time Machine interface
Using Apple’s Time Machine interface is perhaps the quickest way to restore a file in macOS. To do this, simply go to the file’s location (or where it is supposed to be) in the Finder, and then enter Time Machine via the Time Machine menu. You can then use the arrows or the timeline along the right-hand side to locate the desired backup, select the backup file, and click the Restore button to copy it back to your drive. When you do this you have the option to replace the current file, or keep both.
This approach is perhaps best for restoring individual documents and folders in your home directory, in the event you accidentally deleted one, or it became damaged, or otherwise needs to be replaced.
Through the Finder
The Time Machine interface only copies files directly from the Time Machine drive to its appropriate destination on your hard drive, and if needed, you can do this manually. Instead of using the Time Machine interface to locate the backup file, you can navigate to it in the Finder, and then copy it accordingly.
If you have a local hard drive as your Time Machine device, then you can access it directly in the Finder sidebar. If you use a networked backup disk like a Time Capsule or other NAS, then mounting its drive on your Mac, followed by opening the “.sparsebundle” disk image. This will mount the image in the Finder, where you can navigate to the desired backed up file.
In both of these situations, when you copy the file, do so by selecting it in the Finder and pressing Command-C. Then go to its location on your main hard drive and press Shift-Option-Command-V to paste it in this location, but doing so with administrative privileges to preserve its ownership and permissions settings. This will require you authenticate as administrator for the copy, but will ensure the file is restored as-is on the backup drive.
This approach may be best for restoring individual damaged system files, or those installed by third-party applications. While reinstalling can also do this, sometimes if you have altered a specific one then you may be able to replace it in this manner.
Restoring an entire backup instance
The last option is to use the utility on the OS X Recovery partition to restore an entire backup instance to your hard drive. In cases where you have damaged system components, or perhaps need to revert to a prior system version after recently upgrading, then restoring a backup may be the best approach. To do this, simply reboot with Command-R held down at the boot chimes to load the system into Recovery mode, and then select the option to restore from backup and follow the on-screen instructions.