Whether or not your child needs a ticket, or even a seat, and how much it costs depends on where you're going, the number of kids, and their ages.
You can travel with one1 infant in your lap without a purchasing a ticket if:
You'll need to purchase a ticket for your child when you:
Travel Within U.S.
Delta does not offer discounted infant and child fares within the U.S.
Travel Between Countries
You may find discounted child fares when traveling outside the U.S. or when traveling between certain countries. The price of the ticket will depend on the age of the child. Taxes & fees may also apply to infants held in the adult's lap.2
1Number of Infants per Adult—A limit of two infants, less than two years old, per adult may travel together.
2International Taxes & Fees—For infants under the age of two and held in the adult's lap, the cost is usually about 10% of the adult fare plus any international taxes and surcharges, which can be significant.