Others might have different methods, but I backup the following two folders:
- The ebook folder (the folder calibre links to to access your ebooks), and
- The %appdata%\Roaming\Calibre folder which contains all the Calibre settings. (Windows PC)
If done correctly, you can reinstall Calibre, restore those two folders and the library is up and running quite quickly. All addons and settings exactly as they were at the time of the last backup.