I did a lot of research regarding flying with baby and here is what I'm happy to share with you. Please heed the disclaimer that you should check with your own airline about their policies as they do vary quite a bit!!
Baby's Ears: We all know we have to pop our ears during ascent and descent to avoid discomfort and possible damage. Whether this is by chewing gum, yawning, holding our nose and blowing, etc. Unfortunately, baby can't do any of these things. So, it's recommended to have them nurse or drink from a bottle during those times, especially descent. If they won't drink anything, at least see if they'll suck on a pacifier. Anything to get that jaw moving, which will help the ears pop. At 6 weeks, my little one slept through the first flight, door to door. On the return flight he was awake during the descent so I nursed him. He never did show any signs of discomfort.
Carry-Ons: Most airlines give you a freebie carry-on for baby - usually EITHER a car seat OR a fully collapsible stroller. This is in addition to your regular freebie carry-ons of one bag and one personal item. The car seat is great if the flight isn't fully booked, as you can use the seat next to you if it's empty! Otherwise, it can be checked at the gate, as the stroller would be. If you're traveling alone as I will be next month, I highly advise wearing baby in a hands free carrier and checking everything but the diaper bag. Dealing with more items seems like it would quadruple the stress load. Also, keep in mind baby has to come out of whatever they're in for the security check. Yes. Annoying but necessary. No body wants a suicide baby bomber to go unchecked! Don't forget about the 3-1-1 policies for liquids if you have a formula fed baby. As we're exclusively breastfeeding I haven't done any research into what's allowed with that.
Lap Child vs. Ticketed Child: On domestic flights, you can register your under 2 year old child as a lap child and they fly completely free. You can use an FAA approved car seat (it says on the side if it's certified) in the seat next to you if it's empty, still for free! On international flights, you pay something like 10% of your ticket price for a lap child. Not toooooo bad. So why would you consider buying a full-fare ticket? Well, for one, SAFETY. For another, they get the same free checked baggage allowance as anyone else with a ticket. Probably not worth it if that's the only thing you're considering, but worth factoring in. Personally, I am a total cheapskate and go the lap child route and hope for the best.
Child Abduction Precautions: For a domestic flight, if both parents are traveling together, baby doesn't require any documents, though I would recommend bringing a copy of the birth certificate just in case. If traveling abroad, of course they need a passport, more on that below. If only one of the parents is traveling abroad with the baby, Customs and Boarder Protection "strongly recommends" a note from the non-traveling parent stating "I acknowledge that my wife/husband/etc. is traveling out of the country with my son/daughter/group. He/She/They has/have my permission to do so." I would recommend this kind of note even if traveling domestically, and am planning to do that when I travel alone with my son next month. Also, be sure to check the requirements of the country traveling to, apparently Canada has very strict laws about paperwork needed and you will not be allowed in without it!
Baby's First Passport: When applying in person, both parents and the child applying for the passport must be present. If both parents cannot be present, a notarized statement from the absent parent must be presented at the time of application. This is serious business folks! And not every post office has the ability to take the photo there. So, do your research. If you have to bring the photo yourself, note that there can be no one else in the photo, and baby must be looking at the camera with his or her eyes open. Good luck with that if it's a newborn!! They also have specific requirements for the dimensions of the face, etc. I wouldn't trust the local Rite Aid to have a clue how to get an infant's photo, but if you shop around you'll find places advertising infant passport photos. For example, Brooklyn's Photofaction at 117 7th Ave. The State Department has some tips here which include laying baby on a plain white or off-white sheet. They even have a photo tool that helps you crop it to the right size - super easy!! Here is the passport application, and here is where you can find your nearest passport acceptance facility.