Everyone else has given several good ideas, but I have a few to add.
I've flown twice with Mackenzie - we flew to and from Massachusetts at 2.5 months, then to and from at 7 months. I was alone with her the first time, and my husband was with us the second time. We'll be going again in July-August, which would be 14 months.
If you can afford it, get the extra seat - holding a 2.5 month old was easy. Holding a 7 month old was harder. We're getting a seat this time - we'll be flying there alone, then back with my husband.
Check as much as you can. If you get a seat for the kiddo, he/she gets 2 bags as well. But be sure to save at least 1 bag worth for things you're bringing back with you - even if you get no gifts, things never pack as well!
Roll the diapers to make them fit better in the diaper bag - and pack a day's worth (8-10 if possible) plus an extra shirt for you and an extra outfit for kiddo. I don't know if it's the air pressure or what, but we have had our worst blow-outs on planes!
If you bring a stroller, gate-check it - it will get you to the gate, then you can ditch it. That way it can help you carry diaper bag, baby, and sling through the airport.
Listen to my one word of advice - I don't care how addicted you are to your computer - do not try to carry baby, laptop bag, and diaper bag alone! It really isn't worth it - it gets bulky and heavy and cumbersome. but if you have a helper traveling with you, by all means bring the laptop!
Finally, if you have a high-energy child, board *last* - if you pre-board that's just a longer period of time for them to get upset!
Rachel - who successfully cloth diapered through 2 airplane trips!
Thanks to Rachel for this Frugal Baby Tip!
Photo credit: Crazy baby on a plane, by madgerly on Flickr
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