Typical greeting could go...
"O-genki desu ka." would translate to "How are you?"
The response to that would be "Genki desu."
Note that the O is respectful and should not be applied when refering to yourself.
When meeting for the first time, the term "Hajimemashite" is generally used. This is translated literally as "How do you do?" but is a formal and respectful way to greet someone you're meeting for the first time. Often a person may say "Doozo yoroshiku" along with Hajimemashite, which basically translates to "Please regard me favorably."
A typical meeting could look something like..
B: Hajimemashite. Doozo yoroshiku.
A: Doozo yoroshiku.