Traveling with infants under the age of 2 is always free of charge for flights. There's only a small tax you have to pay for the infant to sit on your lap even though they don't have their own seat.
TIP: For flights over 2 hours if you arrive at the airport early enough, when you check in you can ask at the check-in counter to have a bassinet seat on the plane and they will give you the seat with the extra leg room space. This gives you enough room for yourself and the baby to stretch out, or if you have a travel bassinet you'll be able to let your baby sleep in front of you in this spot. Its free of charge!
A stroller is free of charge on the airplane. You can have your stroller checked-in as soon as you arrive at the airport. But if you're anything like me and don’t want your child to run around crazy in the airport or your infant isn’t yet able to walk, they will take your stroller at the gate when your boarding the plane. When you exit the aircraft after landing, you'll receive the stroller again either at baggage claim or outside of the aircraft exit.
A car seat is free of charge. Most travelers check this in when arriving at the airport. If your child is a lap child you won't need the car seat because they’ll be on your lap. If your child has their own seat it will be to your discretion if you want to lug along a car seat onto the plane. I find it much more difficult when lugging our own car seat while traveling. In fact, the only time I bring a car seat is when we travel to a relative's house without kids, and we know we have to do a lot of driving around. We normally take public transpiration or if we rent a car we can ask in advance for a car seat to avoid extra luggage to carry around.
A baby bag is free of charge. A baby bag is free of charge. Fill your baby bag with all the necessities that you need traveling with your infant. In our baby bag, we bring 2 bottles of water. One for myself and one for the baby. Just don't take advantage of being allowed to bring liquid in your carry-on baby bag and think you can bring a 20 case water bottle for a 3-hour flight. Security will throw most of it out. As well, we bring a cool lunch box with a bottle of milk and any of her favorite snacks our daughter enjoys. Try to avoid bringing foreign fruit if you're flying to other countries because by law it's illegal to bring foreign fruits across borders. Many times I've cut up fruit and placed it in her bowl with a lid and it was never a problem, but you don't want to chance the only food you have for your infant.
TIP: After your child reaches the age of two, airport security gets more anal on what you can bring for your the toddler in your personal bag such as water bottles. They figure they're old enough to eat or drink things that you can purchase once you're past security.