Creating the Environment
In a public library setting it can be easy to conduct programs and forward information that reflects back to us and affirms our world view. The conversation about disinformation begins with listening first, then sharing with our patrons about how to vet a news source, where does this person usually publish their articles, is there already a built in bias, does the publication check a reporters sources, are there other articles, data sources or authors cited to support an argument. But to be fair, most of this type of material is written at a higher level and can be seen as condescending.
We use social media and e-newsletters to share information out to our community. We also do a lot of speaking to community groups.
A much lighter touch is to share programming that presents different points of view and
partnering with our local schools on programs that develop empathy through shared story telling. The issue on a local level is getting people to open up to different points of view and to not feel threatened or judged because of their opinions, to discuss the issues they disagree on and not to attack the person talking. To do that requires a deft touch and a lot of diplomacy and patience. One of the first programs we used to do this was a Death Cafe. It brought in people of all ages and was structured so that there was a lot of conversation and a lot of listening. The common ground was death, and the conversation allowed for discussion of all points of view regardless of experiences or beliefs. I have never seen anything like it, just a room full of people sharing their points of view.
I know this is not exactly what you had in mind, but I think in a public space you can create an environment or a safe space where your community feels comfortable learning. Where common ground is created organically and there is trust built to discuss the credibility of resources and sources. Without these first steps the teaching part of our mission will be ignored.