Mr Phoenix, your source was correct. "How do you do" is a greeting used only when meeting someone for the first time. It is not so rare. In fact, I use it often when meeting people for the first time. Though it is a question literally, it does not function as one. The phrase is simply an established convention. The smoothest response in every case would be, "Nice to meet you." Mr. ___: "How do you do, Mr. Phoenix." Mr. Phoenix: "Nice to meet you, Mr. ___" "How do you do" is not the same as "How are you." Mr. Maxey's answer is absolutely correct for "How are you," but not for "How do you do."

Formal: "Fine, thank you. And yourself?" or (less formal) "Fine, thanks. And you?" Very formal: "I'm doing find, thank you. And yourself?" The second response is perfectly acceptable. Very few (if any) English speakers would expect to be completely formal unless you are meeting a head of state.

it is supposed to be "how do you do ?".but i think it is seldom used or say in modern days,you may as well "how are you".