Well, "How do you do" when meeting a certain type of people socially or for business.
The response is to respond with the same question.
I.e.
-How do you do? (extend his hand)
shake the hand and say:
-How do you do?
(Note: Nobody actually responds to the question! Strange, isn't it?)
It is the sign of a well-bred polite English person to respond in this way. Whatever you do, don't say anything else - it singles you out as a foreigner and/or not well bred person. I am not sure if this is used in the USA or not. I can't remember hearing an American say it, but I don't meet a lot of Americans on the other hand, so I might have just missed it.
(This is more of a "male" thing. Women can say shake hands and say "how do you do" in business, but socially, with people who greet in this way, it's best to just smile, nod and mumble "How do you do?" This type of people sometimes "air kiss" strangers too. Just go along with it, even if you don't know the person. First left, then right chin.