In English, it is usual to ask "How are you?" as a salutation. How can I say a similar thing in Italian?
IMHO the other answer is translating "how are you doing". If you are unsure what register to use etc., you can use "Tutto bene?". It's not as common, but it's never wrong: in Bakuriu's example, "Buongiorno professore, tutto bene?" is as formally correct as such a question can possibly be.
Be careful, Italian "Come stai/sta?" is indeed asking about health or state of mind. Most likely, I would use it only if I know that something happened to the person in front of me. English usage of "how are you?" is closer to Italian "ciao", isn't it? "Come va?" could be ok, if it is told with a salutation tone, so to speak.