A new front end module is create with:
At first, enter the title, and only then select in "Module type": 'Miscellaneous'-'Banner'. It changes the form fields. In 'Banner Categories', now select the previously created category, then 'Save and close'.
Now, the front end module must be included in the layout:
Include in 'Included modules' the just-created front end module (e.g. to left)