Both casual and polite greetings are often followed by
(or combined with) questions which ask about someone's
general condition. Responses to these questions differ
according to the formality of the situation.

In formal situations, the typical question is "How do you
do?" and, in American English, the response is generally
the same: "How do you do?" This response is normally
said with falling intonation and is not really intended as
an answer to the question. Instead, it's a kind of "ritualized"
response: no truthful answer is expected. If an answer is
given, however, what's expected is "Very well, thank you."
(Because the speakers in a formal situation normally don't
have a friendly relationship, any other answer--especially
a negative one--would make the person who asked the
"condition" question uncomfortable.)

In polite (but not formal) situations, "condition" questions
are generally some variation on "How are you?" ("How are
you, [name]?" / "How are you, [title]?" / etc.) The expected
answer is some variation on "Fine, thank you" ("Very well,
thank you" / "Fine, thanks" / "Well, thanks" / etc.), but if the
persons asking and answering the questions know each other
well, a neutral or even a negative answer is possible:

In such a situation, the person asking the question will
probably say "I'm sorry" or "I'm sorry to hear that" or
"That's too bad" and expect some comment on a neutral
or negative response, but a long description of why the
other person is not "fine" is not expected.

In casual or friendly situations, "condition" questions may
be answered positively, neutrally, or negatively. Normally
the question is answered without adding "thank you" or
"thanks" to the answer:

In friendly or casual situations (since the two speakers know
each other well), it's appropriate to discuss why the person
spoken to feels the way she / he does--whether positive,
neutral, or negative.