The procedure and the factors a court considers are set out in the Ohio Revised Code (R.C.) There is case law that further explains how this law is applied, but the statutes themselves at least will give the layperson a better understanding.
Juvenile Court statutes are found, mostly, in R.C. Chapter 2151. R.C. § 2151.42, in discussing orders granting legal custody says: "(A) At any hearing in which a court is asked to modify or terminate an order of disposition issued under section 2151.353, 2151.415, or 2151.417 of the Revised Code, the court, in determining whether to return the child to the child’s parents, shall consider whether it is in the best interest of the child. (B) An order of disposition issued under division (A)(3) of section 2151.353, division (A)(3) of section 2151.415, or section 2151.417 of the Revised Code granting legal custody of a child to a person is intended to be permanent in nature. A court shall not modify or terminate an order granting legal custody of a child unless it finds, based on facts that have arisen since the order was issued or that were unknown to the court at that time, that a change has occurred in the circumstances of the child or the person who was granted legal custody, and that modification or termination of the order is necessary to serve the best interest of the child."
There are two really important things to note in the above passage; 1) That the order granting legal custody is"intended to be permanent in nature" and 2) that in order to grant any motion to modify the current order the court must make two additional findings.
The court must find that: 1) A change has occurred in the circumstances of the child - and 2) The modification or termination of the order is necessary to serve the best interest of the child See R.C. § 3109.04(F). This means that even if the parent that lost custody is doing better, the court is unlikely to modify custody where the child's circumstances have not changed.
Another article by this author is linked below and discusses all of the "best interest" factors.
Sign up to receive a 5-part series of useful information and advice about child custody law.