Thanks to helpful videos on the internet I was able to replace the broken chain on my son Noah's bike without any trouble at all. It works great now. It actually went a lot faster than I expected.
I tried to sign up for a basic bike repair class a Broadway Bicycle School in Cambridge, but both classes they offer on site are already full. I tried Bikes Not Bombs in Jamaica Plain, too, but their class isn't scheduled yet. I'll keep looking. (Broadway offers another class though Cambridge Center for Adult Ed that I need to check out.) I guess a lot of other people are interested in fixing their own bikes, too, which is a good thing.