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.
Some people and some regions may well tend to use "How do you do" more than others. "How do you do" is generally considered to be very formal, however, I'd say the use of "How do you do" depends to a certain degree simply on personal preference and regional tendencies. I don't hear it too often in my neck of the woods, but I do know some people who use it.
There is is an interesting example of "How do you do?" here:
(Start listening at around 1:15. That's where he meets his father for the first time, and introduces himself.)
