Get the okay to travel from your pediatrician if your baby is just a few months old. Bring extra blankets. Don't forget a baby carrier or stroller to navigate through the airport (you can check the stroller). Never fly with a hungry baby. The TSA allows bottles of juice, breast milk, formula and of course breast feeding (the 3.4oz liquid limit doesn't apply here, and they don't need to be in plastic bags). Bring or buy snacks. Another well-known trick to avoid the pressure change that often causes screaming babies is to make sure your baby is drinking something during take-off and landing.
Options for safe travel with your baby include keeping your baby in its own car seat, or for babies over 22lb, buy a child seatbelt strap add-on such as this one with rave-reviews called CARES. Check with your airline, but most allow babies under the age of 2 years old to ride on laps for free. While this saves money, and is a common practice, do your research to help make this very personal decision. Remember to check your car seat (for free at most airlines!) so that in case your luggage is lost, you can still leave the airport safely with your baby.
Make sure to bring some super cool new toys, (keyword = new...or forgotten about), to capture your baby's attention by pulling them out one at a time. Depending on their age and how aware they are of their surroundings, this could mean a Baby Einstein Baby MP3 Player (worked wonders for us at 4mo), or a few new DVD's with their favorite characters (which would be the plan now at almost 12mo). If your baby is teething, bring plenty of chew-toys and teething tablets! And very important -- get to the airport much earlier than usual to deal with all the security and check-in procedures that take more time with baby along.
Good luck, mamas! Just remember...if your baby is not feeling well, sleep-deprived, hating the plane, or just in a bad mood -- you'll probably never see these people again, so just smile and stay focused on your little one.