How can I tell if my teen has an addiction?

Change in habits. Watch for change in habits, hygiene, able to give detailed account of activity and temperament.
Altered mental stats. change in personality, or activities. distancing from family, moodiness, unusual smells, dishonesty, car accidents, secretive behavior or need for extra $, unmotivated. Drop in grades, overall disinterest in things he used to like. It is important that you not make the accusation unless you can prove it, so buy a urine drug screen test at the drugstore and check his urine first to confirm.
A discussion? How about a discussion? What does your teen say? Why do you suspect an addiction? Drug abuse and dependency (addiction) are two different things. I wonder what drug(s) you suspect your teen of abusing? If it were my teen, i would try and do what ever it took to get in between my teen and drugs. Drugs like opiates, as well as others and especially when used in combinations can be deadly.