Standard greetings and their responses should be taught in school. I mean, if you learn a foreign language, you learn how to greet someone many different ways, then a series of possible responses and when it's appropriate to use them. Why not in our own native language?
Formal response to "How are you doing?"
"Fine, thank you. How are you?" (For men, there's usually handshake in there somewhere.)
Informal responses,
"Alright. How are you?"
"Not too shabby."
"Pretty good. How about you?"
"Fair to middlin'." (This one might be specific to my own family)
Sometimes, if the person is someone you've known for a long time, an old friend, you can ignore the question and respond with your own, "S'up?"
The way it worked for me... it seemed that everyone around me had a script they all knew, but I had to make a list of greetings and learn them on my own. It's true, I feel like an actor when I speak these lines, but everyone else is speaking the same lines, so no one really knows the difference.
Jerry Seinfeld does a bit about greetings in the workplace. After you say hello to someone in the morning, do you have to keep greeting them all day every time you see them? He observed that for most people, the greeting becomes more and more informal as the day goes on, Good morning, becomes Hi, then Hey, eventually becoming a head nod, and after that you pretend not to see the person, because you've run out of greetings. He suggested that you say "Good morning" to someone in the morning, but for the rest of the day you can simply say, "Acknowledge," when you see them. How sweet and simple would that be?