A letter of consent, preferably in English and notarized, from the other parent or signed by both custodial parents. The letter should say: "I acknowledge that my child is traveling outside the country with the name of the adult with my permission."
You don't need any documentation. The only time you would need a birth certificate is if you were flying with them as a lap child. I just flew 3 southwest flights with my four year old and he was only asked what his name was by TSA. Didn't have to show anything.
TSA does not require children under 18 to provide identification when traveling within the United States. Contact the airline for questions regarding specific ID requirements for travelers under 18.
Children under 18 don't need an ID to fly domestically but do need a passport for international flights.
How do I write a consent letter for my child to travel? List your child's name, birth date/place, and passport details. Provide the parent's/guardian's name, custody information, and passport details. Add contact information for the non-traveling parents/guardians. Detail the child's destination and dates of travel.