How do you do?
This is not a question. It is another, very formal way of saying "Hello." It is also very British.
The correct response is;
"Pleased to meet you." or
"How do you do." or
just "Hello."
We only really use it the first time we meet someone.

How are you?
This is a question, but the person asking it doesn't really want to know the truth about your aching back or hangover.
A polite response is;
"I'm fine thanks. And you?"

Thanks Cikgu. :)
BalasPadamoh interesting.. i think i learned something new today.. thanks for sharing! =)
BalasPadamTo jfook and kenwooi :
BalasPadamYou are most welcome.
oh, never know that. thanks cikgu. =)
BalasPadamAssalamu'alaikum,
BalasPadamI think learning english is a challenge but teaching english is more challenging, don't you think so cikgu?
Thanks a lot for the informations. It really helps us a lot.
Hope to learn more.
=) I love this one. Thank youuuu cikgu!
BalasPadamIs there an 's' for informations??
BalasPadam