Direct the cheating student to stay after class. Tell her you have something very important to discuss. The British Council suggests that instructors "keep it private" when reprimanding students to avoid classroom confrontation.
Show the student the evidence you have of the cheating. Actually showing the student evidence is very important. According to a study done by Rutgers University's Management Education Center, out of 4,500 students polled, "75 percent engaged in serious cheating." Because cheating has become so commonplace, explicitly showing evidence is necessary.
Dole out the appropriate punishment. Most (if not all) schools and classrooms have a policy that prohibits cheating. Make sure the student understands you are punishing the act itself and why the behavior cannot be repeated.
Remind the classroom of the cheating policy the next day in class. Do not mention the incident unless the cheating is class-wide; mentioning the cheating student will only alienate him.
Bring in the principle to talk to your class if the cheating persists. Bringing in an outside authority shows students you are serious about the problem.