What is the correct response to "How do you do?"
Is it "How do YOU do?" or maybe "Nice to meet you, too."
Doesn't it mean "how are you doing?"
"How do you do?" is the standard response, without stressing the pronoun. You could also use "Nice to meet you, too." It doesn't mean the same as "how are you doing?"; it's just a formula for the first introduction to someone, not an enquiry about the health and well-being.