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.
Do you need a notarized letter to travel with a child alone? In most cases of a single parent traveling out of the country with their child, the answer is yes you do need a notarized consent to travel letter. You can download your own customizable travel consent letter here.
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.
Children under 18 don't need an ID to fly domestically but do need a passport for international flights.
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 should obtain a child travel consent letter granting you permission from the absent parent to leave the country with your child (having it notarized is not required, but highly recommended).
Typically, minors under the age of 18 do not have to present identification for domestic U.S. travel. Airlines will accept identification from the responsible adult on behalf of the minor(s).
A parent who frequently crosses the border by land with a minor should always carry a letter of permission from the other parent. A parent with sole custody of the child they are traveling with should carry a copy of the custody document.