Yes, anyone who has studied French has learned the "rules," but there
are so many "what ifs" that I have never fully mastered the concept.
The concept is simple: there are as many exceptions as there are rules, and no school will teach you them because it's all about attitude, individual behavior, and context. And what's more, it evolves over time. What was considered polite 30 years ago can be seen as old-fashioned and outdated today.
The basic rule of thumb is that if you don't know someone or don't know them well, you say "vous."
If it's family, a colleague, a friend, or someone you know well, you can generally say "tu."
You might think that children should say "vous" instead of "tu" when addressing unknown adults. This is a commonly accepted rule. But in practice, if they says "tu" instead of "vous," it will be considered cute.
There is a trick to avoid this dilemma when you don't know whether to say "tu" or "vous," and it's common to hear it when living in France. It's to replace it with "il" (he) or "elle" (she).
For example, you've been going to the same bakery for many years. The baker knows you well but doesn't consider you "intimate," not knowing if he can say "tu" or "vous". He will say "- Bonjour" (without ever adding "Monsieur" or "Madame") and ask:
"Comment il va aujourd'hui?" (How is he doing today?)
And you can answer "- Il va bien, merci" (He's fine, thanks)
Easy, right?