On domestic flights lap infants under the age of 2 not occupying a seat can fly with an accompanied adult at no charge. The age of "adult" is determined by the airline. Southwest allows lap infants to travel with anyone at least 12 years old, JetBlue with anyone at least 14 years old, while other airlines require the "adult" to be at least 18.
If you would like to have your child sit in his/her car seat during the flight, occupying their own seat you will be required to pay for the seat. If you are flying a US carrier the price will be the same as an adult fare. However, unlike US carriers a lot of International airlines really try to making flying with young children easy. This includes a discount for kids aged 2-11, the discount varies but is typically 75% of the adult fare.
Only 1 lap child per adult is allowed. If you are traveling alone with two children under the age of 2 you will have to purchase a seat for one of them.
If you are two adults traveling with two lap infants you will not be allowed to sit in the same row. Most airline rows only have one additional oxygen mask so you will be in rows seated across from each other or wherever another seat is available.
On international flights lap infants under the age of 2 not occupying a seat are required to pay the taxes for the flight at minimum. Some airlines also charge 10% of the adult fare so be sure to check with the airline you are flying.
Same rules apply for car seats and two lap infants in one row, as above.