The best way I've seen to teach this kind of thing is a boot camp. That is, set up a graduated set of exercises, and have the participants work through them. Pick a popular free database (MySQL?) and have everyone bring a laptop with it. Maybe you have to pair people up if some don't have laptops. Give them a set of data, have them set up a schema and import the data. Then have them do some interesting queries over the data.

If you have enough time, you can give them another set of data to import, maybe into another table to do joins over. Or another set of data to merge into the first. Make sure there's examples of bad or incomplete data, and/or examples of duplicates and almost-duplicates. Or whatever you think is the first handful of problems they'll need to solve in the real world. (Give them some sort of zip-code to political district mapping, and have them match constituents to representatives, or something more appropriate. Compose a letter to each representative saying, "We have xxx members in your district who care deeply about this issue." Filter out the ones where xxx is less than 10. Or whatever....)

Make sure you have plenty of online reference material readily available. FAQs, tutorials, examples, etc. Start the exercises off easy, so that everyone will have some success. Make sure they get hard enough that no one will do them all. Make them as relevant to the topic as you can. Start with a short introduction to the exercises, but mostly let people work at their own pace. Have your experts circulate and point people in the right direction. (Don't teach "databases" per se, rather just jump in to using it as a tool. Let the exercises guide the learning.)