I used to serve on boards. My recommendation is that you not worry about committees and organizational structure. You aren’t going to be in a position to have any influence on that stuff at first, and you don’t need to know it to follow the chairman’s directions, and if you disagree with the chairman and the structure knowing what’s in the text books won’t help you.
Concentrate on understanding the financial statements, the agenda, and the resolutions.
Get out! Get out now! Write them a check, wish them well, and support them from a blissful, ignorant distance! Run! Save yourself!
I’m only half kidding. While I value the time I’ve been on non-profit boards, there are times that I should only talk about with a qualified therapist.
Other than that, in my area, there is a non-profit organization that gives classes to other non-profit boards (as a group) and board members as individuals. I would be surprised if there weren’t something like that somewhere near you.
Depending on what kind of organization it is, you may want to reach out to a local college or university that offers graduate degrees in administrating your type of organization (MPA, Masters of Arts Administration, Masters of Museum Studies, etc.) they might know of resources for board education.
Find out about other similar organizations (size or location or mission) - these days, almost everyone has a lot of stuff available on their website. Some of it is even useful. That may spur on ideas. You can also write and ask for help (people who run non-profits are often either nice, deeply convinced of their own expertise, or both. Either trait will often get you an answer back provided they’re not drowning themselves).