You are right, @WilliamVZ. The answer to "How do you do? IS "How do you do?". Note that the function of the set formula "How do you do?" is NOT the same as "How are you?" or "How are you doing?". These other expressions are questions and they do require answers, along the lines of "I'm fine, how are you?" or "Very well, thanks, how are you?". These other questions are polite requests for information about your health or well-being. By contrast, "How do you do?" actually 'means' "I'm pleased to meet you", so the correct response is to echo "How do you do?". This means "I'm pleased to meet you, too". It is used in formal situations when you meet or are introduced to someone for the first time. The conversation might go like this. Mr Brown: Mr Black, this is my colleague, Mr White. Mr Black: How do you do, Mr White? Mr White: How do you do? I hope that's clear.

I think Dana is correct, although there is something that seems strange to me about answering a question with a question, if you are giving a greeting. "Fine thanks, how about you" is probably the most commonly heard answer I know of to "how are you?" But, I would never use the expression "I'm good" but I know many people do say that. Maybe it's just the generation I come from. I don't know. Younger people say that I suppose. I think that answer crept into the language in the late 90s. Who knows? I do like "how do you do" much more than the common, "how are you?" The latter is a terrible expression because it's so awkward. The person asking /making the greeting doesn't really want to know your troubles or worries and the questions always seem to beg a positive (and often false) answer, like "oh just fine, thanks." Doesn't matter if you've got any number of problems or had a horrible day. So, it's one of those little greetings I'd like to see go away in English. I tend just to think of it more as meaning "how's it going" which is probably a better opener. Maybe that's just because " how is it going" reminds me more of the German, which sounds a lot better to my ear.

Hm, I would say if you are shaking hands or the interaction is short, you can respond with "how do you do?" If it is longer, like you will continue to talk afterwards, respond with "I'm good/fine, how are you?"

I’d answer “how do you do with” with “pleased to meet you too” or something that’s not identical to the question asked. It’s avoids the repetition and means the same thing. Hence, I think it’s stylistically better.