Don't be late. Your overarching goal should be to keep the peace. Since actions speak louder than words, always make sure to be prompt. Tardiness could escalate hostility. If you're constantly running late, you may technically be committing custodial interference, which is a crime in many states.
Have a third party present. For the safety and well-being of you and your child, it may be important to have a third party present. When a neutral third party is present, you and the other parent may be more inclined to be civil to one another and follow the stipulations set out in your child custody arrangement. It can make for a more peaceful exchange.
Use witnesses or surveillance cams. A place where there are plenty of passers-by or surveillance cameras can work to your advantage; video or witnesses can help support your account of how one parent behaved towards you and whether he or she followed the custodial agreement. Having witnesses around can also help to prevent violent or abusive outbursts.
Arrange for the exchange to take place at a school or day care. If it's best for you and the other parent not to see each other, then consider exchanging the child at school or day care. Another option is to pick up the child from his or her babysitter or nanny without the other parent present.
Stay near a police station. It may be wise to handle the exchange near a police station in case the situation escalates and you need to call the cops. Exchanging your child inside the police station isn't ideal because it can be scary for young ones, but if you are fearful for your safety, exchanging at a police station is a viable option.