by Mr. Bob
The common reason for the confusion regarding how best to reply to the greeting: “How do you do?” comes from the fact that the question itself is not just about the English language or grammar, but it also touches on etiquette, which is a bit more idiomatic.
More on the etiquette side of things and not so much the language side, you should know that “How do you do?” is actually not a question!
It is a greeting, similar to “Good morning” and, hence, an appropriate reply is also “Good morning to you!”
So, the traditional answer to “How do you do?” is saying “How do you do?” back.
However, it is safe to note that a lot of people, most of them native speakers too, now consider this rule archaic or stuffy.
Such replies like “I’m fine, and you?” or “Very well, thank you. And you?” and other similar variations are becoming increasingly common.
And not one person has been jailed so far for not following the old order of things!