Call the company that issued the card and request a statement from them. That will detail the most recent charges. In addition, ask them to close that card down and re-issue you a new card, so the card in your child's hot little hand will be worthless. Depending on the age of the child, if the child is an adult, I would tell the cc company that the charges are a result of fraud and weren't authorized by you. You could press charges against the child, if the child is an adult, just so the child would know the seriousness of what they have done.
If the child is a minor child, they should have their phone and computer taken away at the very least. Their butt should be grounded into infinity and beyond and their soft little hands should be calloused from the many chores you would be giving them.
The child has committed fraud by using your credit card without permission. Allowing this to go unpunished will only lead to more serious offenses in the future.
