There are many situations that might call for one or both parents to be court-ordered to have supervised visits or exchanges with their child.
The person supervising the visits or exchanges may be the other parent, a friend, family member, or a third party. The reason for the supervision dictates the appropriate level of supervision.
If there is a history of violence or drug use, often a judge will order supervised visits until the problem is addressed.
If a previously absent parent wants to begin spending time with a child, a court may order that the parent slowly transition into a "normal" timesharing schedule. This may mean that the other parent "supervise" or be present while the previously absent parent and the child get to know one another.
If there is no risk to the child in either home, but the parents have a track history of volatile exchanges with the child present, a judge might want someone present when the parents exchange the child.
There are often community non-profit centers that provide supervision services. The fees are usually reasonable and may be income-based. However, often the dates and times available are limited. And, the visits are usually not private; in other words, there may be other parents visiting with their child at the same time in a shared space. If safety and security is the primary concern, this is usually the type of supervision that is required.
In other situations, a third party, such as a mental health professional or an attorney with experience with families and children, may serve as the third party supervisor for visits or exchanges. These visits may occur in a less structured setting, like a restaurant, park, or the parent's home.
It is usually the judge's goal to transition a family to an unsupervised setting. So, even if a person was ordered to have supervised visits in a structured environment, like a community center, they will often be able to transition to supervision in a less structured setting after a successful track record of supervised visits at the center.
Be sure to fully research the providers in your area, including the costs for the services.