How do I retrieve saved files from a backup on iCloud?

Apple offers iCloud Backup for iPhones and iPads but not for Mac computers.

It is possible to sync data from a Mac to iCloud if you turn on those options (e.g., iCloud Photos, iCloud Drive including the Desktop & Documents option). Syncing has some of the benefits of a backup (and the benefit of being offsite) but is not the same as a backup. Major differences include the fact that not everything on your Mac can be synced and the fact that if you delete something, accidentally or otherwise, there is only a limited time period (30 days in most cases) during which it can be recovered.

Also see: https://support.apple.com/mac-backup

And more information on syncing in:

Set up and use iCloud Photos - Apple Support

and

iCloud Drive FAQ - Apple Support

If you have iCloud Drive turned on in your Mac, you access the files by opening a Finder window and use the Finder "Go" menu to go to iCloud Drive. You can then access the files in that Finder window.

iCloud Drive can also be displayed in the Finder Sidebar using an option in Finder Preferences.

You can also access iCloud Drive files using the "Files" app on iPhones or iPads or on other devices by using an internet browser and going to www.icloud.com