"How are you?" and "How are you doing?" would be used with either a friend or somebody that you've met before after some time had past since the last time you saw them. It can be used with strangers, but not usually. "How do you do?" is usually said to somebody you have not met before upon being introduced to them. It is used less these days, but it is still used. More often you hear "Pleased to meet you." in such a situation.

Thank you for your answers.Now it is clear to me)

In the US, "How are you" or "how are you doing" have become common greetings between strangers when the 'how' is stressed. These questions don't necessarily expect an answer. If answered, appropriate responses are "Fine thank you" or "doing well, and yourself?" If the 'are' is stressed, it can be applied to more personal inquiry about how a persons life is going. As fdmaxey has stated, how do you do is becoming outdated.

I am with fdmaxey :)