How does an English person express his condolence to somebody who has just lost one of his family members. What does he say to that person when he sees him?
not a teacher
Where I live, although the form that Mike has given has become more familiar through U.S. TV and film, it is not very common.
A more common expression, in my experience, would be something like: "I'm sorry to hear about your father/sister/brother etc".