Inspired by an excellent post from an IRL friend (yes, I have one of those - her blog is here: http://www.only-mama.com/2013/02/how-to-fly-with-children.html), I decided it would be a good idea to throw my two cents in, as well.
1. Buy a bag to put your car seat in. Not only does it protect the seat from getting soaked if it's raining or snowing when they load luggage, but here's a secret: the airlines never check that a car seat is the ONLY thing in the bag. Don't pack the Crown Jewels in there, of course, but DO throw in an entire pack of diapers and some wipes, plus extra empty disposable sippy cups. They don't weigh much but take up a lot of room, and you'll be glad to have them.
2. No matter how many diapers you have in your carry-on, go pack more. There's no such thing as having too many diapers.
3. Sippy cups make take-offs and landings easier for toddlers and babies. However, be mindful of the fact that all that juice they're sucking down has to go somewhere ... see #2 for how to handle that problem. Also, pack more than one extra outfit for both you and the kid(s) in your carry on bag. You haven't lived until you've spent half a trans-continental flight with your lap covered in warm pee.
4. Road Rules! At our house, that means, "If you've got a decent restroom, you will try to use it, whether or not you think you need to go." Instill respect for Road Rules in the kid early, and you don't have to bargain with them in airports. You just stop in front of the bathroom, say, "I'm invoking Road Rules," the kid groans, and then goes in and pees for 30 seconds straight.
5. You will never regret leaving toy balls at home. You will continually regret bringing them, especially as you wedge yourself under the airport seats AGAIN to try to retrieve them (or have to apologize to the person whose coffee one just landed in). Ditto anything that makes noise. Might be fun at home, but after 10 minutes of sitting near it on a plane, your fellow passengers will be willing to ram it down your throat.
6. "If you can't carry it yourself, don't pack it." And remember, you WILL end up carrying all of your kid's backpacks and loveys and coats and books and whatever other crap they've brought along, despite your intentions to make them carry all their own gear. It's not going to happen without a fight, and this is all about damage control, so just give in and carry them.
7. You can entertain most kids for at least 15 minutes by riding the moving walkways back and forth and back and forth and back and forth. Some kids will do it for close to an hour. Ask me how I know.
8. Travel journals! Make one out of copy paper, folded in half and stapled. Whenever the kid starts whining, hand them a pencil and the journal and tell them to draw a picture of what they see, or something they saw or did. Some of our best scrapbook entries are journal drawings Liza did while on vacation.
9. Don't plan on having ANY time to yourself on the plane or in the airport. If you're not wrangling the kid, said kid will be asleep on your arm, pinning you down beyond your ability to reach that book in the back pocket of the seat in front of you, and by god, nobody wakes a kid sleeping on a plane if they're sane. And even if the kid is watching a movie, you'll be interrupted every 15 seconds for a snack, or a toy, or a kleenex, or to turn the volume up, or turn the volume down, or to clean up a spill, or because they need the bathroom, or because Why Is The Sky Blue, Mommy? Just give it up and go with it. It's four hours of your time - your brain will not explode if you're bored, and you won't be nearly as bored with the interruptions as you would be if you were trying to read.
10. This is supposed to be fun! Try to budget enough time that you can stop to admire the planes and wave to the pilots through the jetway windows. Window shop in the airport stores. Bring a few bucks for crappy souvenirs or overpriced candy. This is a huge adventure for your child, and they should enjoy it. And so should you!
So those are some of my tips for handling the trip. And believe me, since we've been flying back and forth to various places with Liza since before she was one (http://mind-flush.blogspot.com/2006/04/waiting-for-our-flight-in-louisville.html), we've got enough miles under our belts to be relatively good at this. I've lost track of how many flights she's been on - at this point, she doesn't even view it as a treat anymore, it's just a necessary part of getting to the fun vacation or the family visit. In some ways, I wish it was more special for her. And in some ways, I'm just glad she knows the drill at the security line so I don't have to micromanage her every moment. Here's hoping you get there someday, too!