Drag and Drop
The most common method for moving files to a backup, or any kind of
storage, is to select the desired files, drag them to the target
location, and drop them there. TagNBag similarly allows you to
drag and drop files to the To back up.
The files aren't actually moved until you do a backup. But
then, you can repeat the transfer without going through the process of
selecting files.
To set files for backup, you can drag them from the file system to either the To back up item:

or to the To back up view

You can also move the file to the To back up item in the Explorer tree view