Step one is to rule out any physical reasons for a unhappiness, ie, depression. Also, assess if there are any situational reasons for unhappiness: divorce, let down by a friend, recent breakup, failing scholastically or a major disappointment.
Once those possibilities are ruled out as the cause, the first question I would ask your teen is what is his/her perception of happiness. Then, I would ask your teen what he/she feels is keeping him/her from being happy? Determine if what he/she feels will make him/her happy is realistic. For example: If your teen has never been athletic, chances of being made Captain of the Football Team is not likely. On the other hand, would golf, swimming or art lessons help get your teen involved in something doable and travel in a new direction?
The happiest high school students seem to be those who are outwardly focused. They look to get involved; volunteer; join in activities that help others and gets the focus off themselves. Most high schools have many charitable organizations that need help.
If, however, this unhappiness is not new, but has followed since grade school, maybe it is time for professional help. For ex: obesity, failing grades, anti-social personality, drugs, and the like.