Any child under 2 years old can fly free along with the parents when sitting in the parents lap but you must bring a birth certificate to prove the child's age if they're to fly free with the parent.
But any child over age 2 will be charged the regular adult fare but some airlines offer discounts sometimes for children 2 years of age and older but you need to ask the airline about it.
Southwest airlines is one airline that sometimes gives reduced fares to children 2 years of age or older.
But be prepared to pay the regular adult airline fare that you paid for yourself for your child to fly.