I am a frequent traveler and have flown 20+ times with my 4 year old and now 13 month old son. My main piece of advice is just to remain calm during traveling--don't get upset by a fussy, crying or hysterical baby. In the midst of major meltdowns at the airport (and my boys have both had them) I tell myself over and over--"they're just babies, all babies get upset, everyone has either been a baby or had a baby and has experienced this. We'll get through this." That always seems to help me. And a calm mommy helps to keep the kids calm. My other recommendations:
Always bring a stroller. They can check it at the gate for you but it helps immensely in getting around the airport.
If your baby does better in a car seat--bring it. I always ask upon check-in if there are any empty seats on the flight. If so, they will allow you to bring the car seat along and you can strap the baby into the seat once on the plane. If it seems like alot to bring with you, rent a cart there in the airport and load up your car seat, stroller and carry-on and then stick the baby in a bjorn/sling. It is also great to have the car seat on the plane with you as it automatically saves a seat right next to you. You can put your diaper bag there and get in and out of it easily without disturbing a sleeping baby in your arms.
Always bring an extra outfit, bottled water, extra wipes and diapers. Bring enough formula (if using) to get you through one full day (you never know--you could get stuck on the plane for hours.)
Bring a blanket that you don't mind getting dirty. I have had to change my baby on the floor at the front of an airplane many times. Bring plastic bags to put the dirty diaper in. Some flight attendants don't appreciate dirty diapers. :)
Sit near the front (if your flight has open seating)--that is where most parents with kids sit and they don't ever mind a crying baby since they are used to them already.
Finally, make sure you get there early enough to pre-board. Most all airlines let travelers with children under 6 board ahead of time.
Good luck and safe travels.