Is how are you or how do you do right?

How do you do fine sir?
How are you today?

Either just the first one is a bit more posh ;)

"How do you do?"
*tilts top hat and carries on walking*

wwwwwwwwwwwwaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaassssssssssssssuuuuuuuuuuuuuuuuuuuuupppppppppppppppp

Strictly speaking the correct form is 'How do you do?'
To which the reply is 'How do you do?'

Nowadays its considered a quaint form of English, but nontheless, still the correct form of address and greeting upon first meeting.

I don't think either one is more right. I mean, "how are you" makes more sense when you break it down than "how do you do" but both are fine. Anyone who nags at you for the second one being improper is just an irl grammar Nazi.

It depends on context.

How's it hanging?

Pfft.. I hate that crap. They know what you mean, so they can shut up and deal with it. Petty.

I believe "How do you do" is an older form of greeting, probably falling out of favor because it has more words than "How are you" and so many today are so rushed that they can't even spell out you, but type "u" instead. The civilities of the past are quickly fading into obscurity.