What should I say: “Tu vas bien?” or “Vous allez bien?” Sometimes you don’t know well if you should say “tu” or “vous”. As both “tu” and “vous” mean “you” (singular), here are some clues to help you.

TU: Tell “tu” to someone is called “le tutoiement” (noun) or “se tutoyer” (verb). It does not mean you are not polite. But it is restricted to some people. Tell only “tu” and not “vous” with:
1) family. It is very rare and kind of weird that children tell “vous” to their parents or relatives.
2) friends/classmates/students. Sometimes, even if   you don’t know somebody, you will use “tu” become you are in the same college.
3) children. If not, they will think you are crazy.
4) when chatting on the Internet.
5) close colleagues if they are about the same age of you. If not, you may ask them the first time before you can say “tu”. If you are not sure, tell “vous” and wait for them to ask you.

Even if people will may be comprehensive because you are learning French, you may want to avoid awkward feelings and try to use “vous” in every other situation.

To break the ice with new people who seems about your age, you can ask them if you can tell you to each other. If they are older, it is better to wait for them to make the first. Some people prefer to keep the “vous”.
To ask somebody, you can tell:
“Est-ce qu’on peut se tutoyer ?”

VOUS: Tell “vous” to someone is called “le vouvoiement”. Of course, you can use “vous” to speak to one person and you should tell “vous” to be polite in some situations. It is a mark of respect to strangers, superiors, professors or to people you don’t know enough. You should use “vous” with:
1) everybody you meet for the first time unless sometimes young people speaking to each others in a friendly way,
2) customers and professionals. There is no hierarchy status between customers and sellers/waiters for example. All should be equally polite and say “vous” to each others,
3) teachers, professors. And pupils should always say “Bonjour Madame/Monsieur” to their teacher. Just tell “Bonjour” will seem disrespectful,
4) boss, manager, higher authority in a society,
5) in-laws unless they tell you use “tu”. Usually, they will.

Finally, “vous” is sometimes used in an ironical way as when a father call his son, Mister.

NB: be careful, in Quebec, people say “tu” to people they don’t know in the street. In any event, use “vous” when you don’t know. You will look too formal maybe, but it won’t be a mistake as to say “tu” to someone you should not.

You can check the lesson with TU and VOUS: