Seating Baby/Car Seats
If a seat has been purchased for baby, a car seat can be brought onto the plane and buckled into the seat (check airline for size limitations and check your car seat's measurements on this amazing chart). If a seat has not been purchased for baby they will be considered a "lap infant" and the car seat must be checked either with luggage or at the gate. For longer flights ask about having a bassinet. You will be seating in the front row facing a wall rather than the next row of seats. What I would describe as a "baby basket" can be affixed to the wall during flight and will be removed before landing. The catch with this is that Baby must be held during turbulence so... if your baby is easily woken, best to just let them sleep on you and use the bassinet as an extra place to put stuff.
Yes, you do need to bring a stroller-just make life easier on yourself-plus it doubles as a stuff caddy when wearing baby. I HIGHLY recommend "snap and go" systems. The seat can be easily secured into any vehicle (including airplanes) without a base and it all folds up quite easily.
When going through security WEAR the infant using a fabric baby wearing device such as the Moby or Maya Wrap (no metal). Could you just carry them? Sure, but you're going to want your hands free for this next step.
Assuming you're using a "snap&go" style stroller, detach the seat, collapse the base, and place both on the runner to go through security xray. Some security areas will allow the stroller to remain in tact and will subject it to a separate scan. While convenient, this may be more time consuming than it's worth; look ahead in line and follow suit with what other travelers with children are doing.
Boarding the Plane
Purchase 2 "gate check bags" (they're kinda like dry cleaning service bags and fold into themselves quite small) of suitable size for your base and seat (retail ~$15-$20 each). At the gate (door of airplane) bag the seat (if not using on plane) and collapsed base and leave by the door of the plane with LUGGAGE TAGS attached.
When deboarding get comfortable and plan to be the last to deboard, returning of the stowed base and seat may take a while. If traveling as a parenting team, plan to have one parent wait for the buggy while the other and baby find a seat or snack near the terminal.
These pack into their own cases quite well and can be checked with baggage. Check airline as to charge, some airlines check travel cribs, car seats, and buggies free of charge; others do not. MOST (if not all) hotels have pack&plays or even regular cribs so it may not be necessary to bring your own; though I do recommend bringing your own sheet or two for familiar scent as well as your peace of mind regarding cleanliness.
Bringing your own high chair can be a lifesaver if doing breakfast or snack in a hotel room or in an otherwise childless home. It also serves as a place to put the baby while creating a baby friendly space. I recommend one of two styles:
This is one of MANY articles written on flying and generally traveling with baby and primarily covers the question, "What should we bring/buy?" and is based on my personal experience traveling with families and their babies both domestically and internationally. TSA and airline regulations change often so check with your airline as well as friends or family who may have recently traveled with an infant.