You might also find this Wikidata in One Page resource useful in doing a general introduction before you get folks to dive into editing.
Figuring out how to structure organizations and their parent / child relationship is important. As Olaf mentioned, they library system is the overall administrative home and the branch is a physical location -- some things belong with the parent, some with the child. It would be great to model this consistently.
In the work that OCLC did to acquaint librarians with WIkidata, people on that project did an discovery and exploration exercise that I think was good and gave people a chance to explore Wikidata before diving into editing. I can't take any credit for that whatsoever but you might consider structuring an activity like that. I can share a copy of that with anyone who is interested.
Merrilee