Typically you want to take a backup of a root filesystem that is not live. That means either booting from other media or moving the media for the root filesystem to some other computer. And then copy the not-live root filesystem. Either using rsync or using disk imaging.
But often a full backup is not needed. All that is needed may be to backup the configuration and be able to restore it. Often that means just /etc.
There are desktop tools to backup live root filesystems, and restore them, that greatly reduce the need for a full system backup. Timeshift is one example.