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.
Understand that the more evidence you have that shows bad things about the other parent's parenting skills, the more likely it is you will win.
Gather evidence that shows the other parent is unfit and evidence that shows you are a great parent.
Take photographs. 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. Write down the horrible or neglectful things the other parent does and write down the wonderful things you do with your child. Write down what the child tells you happens with the other parent. Include any information about meals, bedtimes, baths, etc. that shows how the child was cared for by the other parent.
Keep track of any visitation that occurs. Write down dates, pick-up and drop-off times and information about what happened during visitation.
Talk to family and friends. Determine if any of them have helpful firsthand knowledge about the situation. Ask those that do to testify for you in court.
Hold on to report cards, counseling reports, medical records, letters or any other written evidence that pertains to your child's health or well-being.
Preserve items such as children's clothes that clearly show neglect or abuse (bloodstains, rips, tears, etc.).
Create witnesses. Get other people to witness things so that it is not your word against the other parent's. For example, if the other parent is routinely one hour late to pick up your child for visitation, have a friend with you the next few times so that someone else can testify about this to the court.