Since my parents live on the other side of the country, and I really enjoy seeing my family, I have traveled with small children many many times. Traveling with an infant is different than traveling with a 3 year old. I am learning to revisit my ideas of traveling. However, here are some tips that I have learned the hard way.
1) If you have a baby, have something for them to suck on when the plane is taking off and landing. For me, it's just easiest to start nursing as soon as the plane starts taxiing. Then, it's common for my baby to fall asleep 15 minutes or so into the flight. Also, it helps the baby's ears to equalize, so they don't hurt.
2) Take a foldable stroller. You can check a stroller or carseat or a travel system (where the carseat clips onto the stroller) plane side. When going through security, the stroller gives you a place to put the child while you load everything else onto the conveyor belt. Then, take the child out and put the stroller/carseat on last. Pick it up as soon as it goes through, put it back together and strap the child in again while you put your laptop back in its bag etc.
3) Check the airport for suggestions on how early to arrive. With children, plan on 15 more minutes. It takes me 15 more minutes to get through security with children than when I'm by myself. If you have more time waiting for your flight, you can wander around the airport and get some wiggles out before the plane takes off.
4) If your baby is bigger than his age, take a copy of his/her birth certificate with you. This is not always required, but if your baby is 18 months old and looks like he's 2 1/2, you'll be sure not to run into any trouble.
5) Limit the carry-ons. With small children, you have your hands full enough. I like to combine my carry-on bag with the diaper bag. Also, I let Jackie carry her own small backpack with her toys and books in it.
6) If you have a full carseat and not just an infant carrier, check it as luggage. If they lose it, the airline must lend you another one. Also, take it from my experiences, carrying a carseat through the airport is unwieldly, heavy, and just plain miserable.
7) Take empty sippy cups and bottles. Fill them up in the airport. Also, most flights have a beverage service. You can get water or juice and fill up the sippy cups with that. It gets hairy trying to take sippy cups, liquid formula or that type of stuff on the planes now.
8) Take advantage of curbside check in. For $2-3 dollars per suitcase (depending on airport or airline), the sky cap will check your suitcases for you from the curb, and you don't have to haul all of your suitcases into the airport. Renting a luggage cart can cost $3.50 anyway, and you often still have to take your stuff over to the x-ray machine even after you're checked in inside. Dropping off all luggage at the curb gives you more chance to help your children inside and help them enjoy the airport instead of giving all your attention to a suitcase.
9) If you're parking your own car at the airport, look around for places you can park just off from the airport and then take the shuttle. It's usually much cheaper. For example, airport parking in Atlanta can cost $15 dollars a day for long term parking depending on which parking lot you choose. Whereas, there are places that have a shuttle service from an off airport lot where you can park for $10 a day and ride the shuttle. Then, the driver drops you right off at the curb. With the curbside shuttle service and the sky cap, you can minimalize your luggage handling.
10) Take early morning or late night flights. Sleeping children are easier than busy children. When we flew home from Utah, we purposely got an afternoon flight thinking that it would be easier to fly at that time when it was more convenient to get to the airport and our kids would be happy. All other flights I've taken with my kids have been late night flights and early morning flights. They're much easier because the kids are tired and the airplane ride helps them hold still. Then, they sleep.