Don't panic.
I know that the thought of flying with little ones, especially a baby, can bring terrible fear to the heart of a young mother. Believe me: I've known it. When my daughter was about five months old, I took her on her second flight, this time sans my husband. We had two connections and to make everything lovely and complicated, at that time, I was feeding my baby pumped breastmilk, meaning I had to find a time and place every few hours to pump while juggling my baby in public. Fairly nightmarish, I will concede.
BUT! Let's not lose hope. Here are some tips and tricks that can help you fly without cause for concern when you're toting an infant along with you.
1: What to expect from the airlines
*You will still have to go through security. Many airlines have a special, expedited lane for mothers with children. Be sure to ask- it can save hours.
*You are allowed to bring a stroller and a car seat (both will be checked as you get onto the airplane itself, meaning you can take it all the way to the door of the plane) at no extra charge. They are not counted as extra baggage. If you have an extra seat on the airplane for your baby, you will take your car seat on board and sit your baby in their car seat and buckle them in for departure and landing.
*You will have to carry your baby, sans blanket, through a metal detector. Your stroller, car seat, luggage, shoes, belt, etc., will all have to go through the scanning machine, while you, barefoot, take your baby through.
*You are allowed to bring breastmilk/water for formula/already mixed bottles through security in spite of liquid restrictions. Additionally, you can bring an ice pack for your infants milk/formula. Often, TSA employees will want to scan your breastmilk/formula/bottles to make sure they are what you say they are- when they do, you can request them to change their gloves and put the milk/bottles on a clean towel, so as not to spread bacteria on them.
*On your boarding pass, it will need to say "infant in arms" if you have not purchased an extra seat and ticket for your little one. If your boarding pass doesn't have that printed, you can speak to any airline employee and they will direct you where you need to go to get it changed.
*Check with your flight before getting on. After making it through security and to your departure gate, go speak to one of the employees that is at the desk by your departure gate. Let them know that you have an infant with you and, if the flight is not full, they will often give you a seat next to an unoccupied one, so you have somewhere to seat your baby.
If the flight is full, request an aisle seat, and one towards the back. You will likely be getting up to change diapers and soothe your infant. An aisle seat makes that easy. A seat in the back, near the engines, can be both calming, due to the sound from the engines, as well as muffle any crying your little one may go through. Not to mention, you'll be near the bathrooms. I guarantee you'll be heading there with baby often!
*You will be boarded first. Those with special needs, including flying with children, are seated first, giving you extra time to get settled in.
2: What to Bring
*Regularly stocked diaper bag (milk, treats, burp cloths, diapers, wipes)
PLUS
-2 changes of clothes for little one
-1 change of clothes for you (just a plain shirt and leggings could be a lifesaver)
-Hand sanitizer
-Sanitizing wipes (for wiping down counters in public restrooms, etc)
-Changing mat (you WILL want to bring your own changing mat for the rest rooms on the plane)
-Extra binkies
-Baby aspirin (you don't want to be caught with an infant getting a fever and no way to relieve their temperature)
3: What you Need to Know
*Some people may be annoyed to see a baby one flight. Most, however, are extra friendly and over the top helpful. Most are parents and grandparents and know the potential trauma of flying with a little child. You can expect many friendly smiles, offers for help, and understanding looks. Far more rarely will you catch an annoyed face.
*You want your child sucking on something during takeoff and landing. The change in air pressure for your baby can be painful and lead to hours of unhappy crying. To avoid this, either be feeding your baby during takeoff/landing, or have a binkie for them to suck on. The sucking can help them to pop their ears.
*It's going to take time. Although airlines in general do quite a bit to make traveling with an infant less taxing, it takes time to get seated, go through security, and deal with any unexpected blow outs. Plan ahead and arrive with lots of time to waste at the airport.
*You will probably not be sitting by a window, watching the clouds go by, thinking deep thoughts. I do enjoy flying, quite a bit, but flying with an infant is a different matter altogether. Your time, thoughts, and efforts will all go to calming your child, holding your child, rocking them, feeding them, changing them, etc. While bringing a good book or Kindle might come in handy, it is far more likely that your every moment on the airplane will be devoted to your little one.
*Don't sweat it! It's a few hours, one day at worst, but it won't destroy your life. Be prepared, take a deep breath, and look forward to arriving wherever it is you get to travel!