dear,I assume How do you do? is FORMAL a formal greeting for someone that you have not met before:Fore instance,"I'm Jack Stewart." "How do you do? I'm Angela Black."
Yes, "How do you do" would usually be something people say when they are introduced to someone.
When I am introduced to someone, I generally do not say "How do you do". My personal preference is "It's nice to meet you." The response to that might be "It's nice to meet you, too." In other words, a repetition of the same phrase -- as Philip has already mentioned.