Family courts respect the finality of custody determinations and generally will not re-open a custody case unless a petitioner can show some substantial change in circumstances, or the discovery of new evidence which endangers the welfare and safety of the child. In these cases a petitioner must file a petition to modify custody, and participate in a hearing on the petition.
Draft your motion to modify custody. You can obtain a blank copy of the motion from your local county or district court's office of the clerk, or online from some state court system websites. While specifics of the form vary from state-to-state, you will typically need to enter the case information from the existing court custody order, full identifying information on the child and current custodian and the procedural history. Include in the motion the new evidence or substantial change that has occurred since the last order that justifies your request for modification, and show how this change adversely affects the health and welfare of the child.
File your motion with the clerk's office, and upon paying the filing fee (which can range between $25 and $150) you will receive a stamped copy of the motion along with a court date on the motion. Use a special process server such as the county sheriff to serve a notice of the petition upon the current custodial parent.
Appear at hearing on your motion. If you and the custodial parent cannot come to an amicable agreement, the court will conduct a hearing on the motion, where you will be allowed to present your case to the court, including any witnesses or evidence you wish the court to hear. The custodial parent will be able to contest your allegations and question any witnesses you present. If the court determines that a modification of custody is in the child's best interests, it will modify custody and appoint you as the custodial parent.