Information about mental hospitals
The involuntary commitment of a minor is a matter of state law, although each state must make sure its processes and proceedings are in accordance with the United States Constitution.
Generally, I would have to say that all 50 states allow the involuntary commitment of a minor and that the minor must be a threat to him or herself or others for this to take place. Once a commitment takes place, there is a limit to how long a child can be kept without a psychiatric evaluation. If the evaluation shows that there is still a danger to the child or others, then the child might be held over for a longer period. I should also point out that a minor's use of drugs and/or alcohol may constitute a danger to the child or others, and that this is a common basis for involuntary commitment. The child is entitled to a hearing if he or she is a danger and unwilling to remain in the hospital voluntarily. The child is also entitled to an attorney.
I would guess that treatment of a minor and therapy for a minor vary from hospital to hospital, but certain principles are likely to apply to all. For example, there is usually some form of group therapy available and limited individual therapy. Many hospitals place a great emphasis on structured activities for patients. In most cases, there is a behavioral aspect to treatment in that patients are expected to follow rules and policies and lose privileges if they do not. A patient who is unable to conform, who "acts out" with self-harm or harm to others could very well be placed in isolation.
Minors, like any other patients, are treated as human beings. They are respected as people, and they are fed, housed, and clothed. They are given treatment that is likely to help them return to their families and their lives.
Often, novels and movies will portray mental hospitals as terrible places, where people are chained to the walls, are tortured, or are neglected. However, I would imagine that in every state, the hospitals operate on sound medical and psychiatric principles, treating their patients as people who just need some help.
I have not provided any links because each state has its own laws. But if you Google the name of your state plus the key words "commitment" and "minors," you will be sure to find a site with the laws and regulations for this process.