I have done a lot of traveling with The Nut. Most has been via plane and the majority of those flights have been just the two of us. Friends often ask for advice when they are about to fly. Here are some bits of wisdom I have gleaned from my journeys:
I always bring a carseat on the plane for The Nut. It’s not because I’m a safety freak, but because I simple can’t tolerate her crawling all over me for several hours. For some reason, she doesn’t seem to question containment when she’s strapped into her own seat. Yes, it’s a headache to lug it through the airport, but I’ve found that it’s worth it. Especially if you’ll need a carseat on the other end, anyway. {You will need to strap the carseat into a window seat, so be sure to ask for one ahead of time.}
If you travel with a stroller (even an umbrella), try strapping your carseat into it like this:
Note: must remind The Nut to throw her butts in an ashtray.
Latch the tether straps around the back of the stroller for a bit of security.
It’s probably not terribly safe or comfortable for long hauls, but it works for getting a kid, a carseat, and a stroller (plus purse and diaper bag) through the terminal to your gate. If you don’t want to put your child in the seat, it’s still a great spot for a bag or two.
You CAN bring drinks and liquid (read pouches, yogurt, etc) snacks for your child. I have always brought at least one sippy cup for The Nut and I have never had an issue. They may ask you to open your container for vapor testing, but I have never had anything confiscated (including my own water bottle) when I am escorting the little one. Just take them out of your bag and place them in a separate bin when sending security.

If you’re flying with a baby, prepare for $hit. Literally. Something about the pressure change seems to impact their little systems. Some planes have changing tables in the bathroom, but don’t count on it. Be sure to bring extra clothes for baby, and an extra shirt for yourself. Someone told me that before I flew the first time and I didn’t want to waste the space. I wore puke for two hours. Not pretty.
Even though my daughter is potty trained now, I still have her wear a pull-up on flights (and long car drives) this prevents the inevitable “I need to pee” during take off or turbulence.
You child might have a melt-down. While some people will shoot you with death rays, most will be nicer that you think. You can always cry yourself if you need to. Been there. It helps.
Bring snacks, preferably non-stinky, non-sticky, and non-crumbly ones. Granola bars, Goldfish crackers, apple slices, bananas, puree pouches, and yogurt tubes are easy ideas. If you have a candy junky, a single lollipop can gives you a lot of bang for your sugar buck (and can be used as a bargaining tool when needed.)
As far as entertainment, I have two huge suggestions:
A) Jetblue Jetblue has a tv for every passenger and they provide lots of free snacks. This cuts your carry on packing to a minimum. Having your toddler soaking up The Disney Channel while you’re absorbed in Bravo? Priceless.
B) iPad An iPad takes up little space and can hold endless games, movies, shows, music, books. This buys us WAY more quiet time than a coloring book or a toy car.
If your child does have a favorite genre of toys (trains, dolls, animals) look for a set of miniature versions. They can set up shop on their tray table and you won’t use up much valuable space in your bag. Stickers also make for a fun, streamline distraction. Just be sure to pack a notepad or some scratch paper so your child has an acceptable surface to stick them to. Wikki Stix (wax coated yarn sticks) are another very portable form of entertainment. For additional pleasure, wrap up a few items (new or old) in wrapping paper or tissue. Just the act of presenting and opening them will provide some extra fun.

Be sure your child is wearing easy to remove shoes and comfy socks. They no longer have to remove their shoes to go through security (ages 12 and under are exempt) but little feet tend to want to kick seatbacks and socked feet make less impact.
Don’t take a red-eye unless you absolutely must. I repeat! Scheduling a flight around your child’s naptime is a great idea. Hoping that you and said child will get a solid night’s sleep while contained in a pillbox is lofty at best. Unless you are traveling in First Class with a nanny and drugs (for yourself!), overnight flights with children can lave you hurting for days.
Not a red-eye, but nap time in first class with a grandma and plenty of cocktails.
Most importantly, keep you chin up and remember you probably have a good reason for flying and it will all be worth it once you get there!