Formal greetings are very important. It is essential to "get it right".
If, for example, your Senior Management visits from England. When he is shaking hands with everyone, you do not want to look stupid.
So, the essentials:
How do you do? <---> How do you do? (use this only at the first meeting)
How are you? <---> Fine, thanks. (or) Very well, thank you!
(use this at any further meetings, but not at the first meeting as it's a little too informal)
Nice to meet you <---> Nice to meet you too.
Do you shake hands?
BRITISH - essential, at work, formal
CHINA - yes, only in business
INDIA / JAPAN - no