What can you do to watch a child to make sure they don't attempt suicide again?

Constant supervision. It's most important to insure the child is in a safe environment - whether at home or in a treatment facility. The parent/guardian needs to be able to provide constant supervision and monitoring. The environment itself needs to be safe: lack of access to weapons, medications (even over-the-counter ones), sharp objects. Ongoing treatment is also crucial to symptom improvement.
It takes balance. Fortunately, strong suicidal feelings rarely last very long, especially in teenagers. But, someone who has made a suicide attempt before is more likely to do so again. If at all possible, partner with the part of the adolescent that wants to stay alive--if there weren't some part that did, he or she would be dead. Have them help think about would will keep them safe if the urge returns.