I've travelled with infants a couple times, and it wasn't nearly as stressful as I was afraid it would be. With my son, he just played on our laps the whole time, and smiled and cooed at the people sitting near us. Actually, one of the people riding right behind us was a flight attendant, and she held him for a few minutes to give us a break. Other than that, he had a hard time falling asleep, but wasn't really fussy about it. I think he was about 7 months old at the time, and it was also a 2 or 3 hour flight. We had a carseat available for him, but we didn't use it. They only fit in window seats, too. But, if you have one and they have a seat available, you can bring it on without paying for the seat. If you have a stroller with a carseat that snaps onto it, use it in the airport and check it at the gate. They will have it waiting for you as you get off the plane so you don't have to walk around with all your carry-ons and the baby, too. We found that we got through the lines faster because of the stroller at bigger airports. They would send us through a separate security check since we had to unload the stroller, fold it up, then take our shoes and the baby's shoes off, etc.
The second trip, our daughter was a year old, and VERY active. The flight was tiring keeping her corralled in our seats, but once again, she wasn't fussy. That was a 5 hour flight, and the flight attendant actually took her and walked the aisles for 10 minutes or so to give us a break. We had books and a few toys with us that she enjoyed. Our son was 3, so we took a laptop and some videos, and that kept him happy for hours.
For both trips, I was still nursing, so I nursed during during take-off and landing to help their ears, and the kids did fine.
Good luck, and have fun on your trip!