When gathering evidence in a custody case, it is important to keep records, take photos and focus on evidence that will show that the other parent is not as good a parent as you. Hire an attorney so you can be sure your evidence will be admitted in court. If you do not have an attorney, hire one for a few hours to explain your state's rules of evidence to you. The rules of evidence are very complicated and sometimes do not seem logical. Gather evidence that shows the other parent is unfit and evidence that shows you are a great parent.
Photographic evidence is very persuasive.
Take photos of abuse or neglect by the other parent. Take photos of the other parent's home, of your home, and of your child's room. Keep a log or journal. Date each page. Record events pertaining to your child in detail.