W.,
Welcome to the world of baby traveling! I started flying alone with our daughter at 8 weeks old and my husband and I have flown with her several times in the past year. Get ready for a long day, but a wonderful learning experience.
My advice to you is to buy your son his own seat next to yours if you can afford it and if it is a long flight. But I know we rarely have due to money, so yes he can sit on your lap for free. When you buy your ticket you will have to say "with an infant" on-line and put his name so they have a record of him. Or tell your ticket agent on the phone. If you do buy his own seat you must have his carseat for him and he can only sit at the window on most planes, so definitely tell the agent.
Regardless of your seat, here are my suggestions for a smoother day (especially going solo):
1) Bring your favorite stroller. If you have delays or stops, your son will spend the entire time in the stroller to give your lap a rest. Also, your only chance to go to the bathroom without holding him is in the airport!!! You will get a tag at the gate and wheel it all the way to the airplane door before you fold it up and leave it there. It will be waiting for you at your next stop.
2) Pack your diaper bag and bring a backpack full of necessities and extras. It will free your hands, which is important. Forget extra bags, stuff for you--that is in the past. :-) Bring extras in the backpack in case your flights are delayed. (I spent five hours in the Chicago airport once...) Keep your backpack at your feet on the plane to make it easy.
3) Are you nursing? Bring your favorite nursing cover or wear your favorite nursing shirt. They sell really good ones. If you are bottle feeding, bring just the powder and buy water at your gate. Most airlines won't allow any liquids through security. (Enfamil sells great travel packs of powder, too.)
4) Nurse/bottle feed during take-off and landing (if awake). It soothes their ears.
5) Going through security...if you are solo, this will drive you crazy! You must fold your stroller up to go through the x-ray machine (they all fit), as well as send all your backpack and coats through--all while holding you baby and taking off your shoes and your baby's shoes. Wear slip on shoes!!! Most security people will offer to help you, but it is still madness. (Another reason to have one backpack!)
Also-- if you are bringing any baby food, you must claim it. Pack all medicines and liquids in your suitcase.
6) At three months, you son may have a favorite type of blanket or toy. If you know of anything he might like additonally, you may want to add it to your backpack and surprise him with it on the plane when he begins to get fussy.
7) Most planes have NO changing tables. Crazy, right? Bring a pad, flip down the toilet seat, and change him on there in the tiny bathroom. This is something you should get a medal for when you're done!
8) If you are holing a baby, simple things like eating and drinking are difficult. Try to eat at the airport during stops or before boarding while they are in the stroller (and do a last minute diaper change). Do not skip any meals that day. You will need all your strength and energy for your trip. Do bring a snack in your bag and extra money just in case you are delayed.
9) Forget about schedules that day. Feed your baby whenever and let him sleep whenever. If he eats or sleeps not enough or too much, it will be fine.
10) Real important: You must drag your carseat through the airport if he is sitting in his own seat. (Travel system strollers make this easy). If you don't have a travel system, just plop it on top of your stroller's lid as you wheel through the airport. If he is lap sitting, put your car seat in a plastic bag and check it as luggage. You will need it at your destination! I know some car rental places rent car seats but I have heard of bad stories (broken, damaged, dirty, out of date), so I recommend bringing your own.
11) Keep in mind most airlines now charge for luggage. You may have to share a suitcase with your child or pay money. Check with your airline.
12) Most of all, relax and try and enjoy these moments, as crazy as they may be. If your baby cries, oh well. Let people look and help if they offer. If you have plenty of time at the airport, lay out a blanket on the floor and let your baby stretch out. You both will need the break. If you have the room, bring your camera and capture your baby's first trip!
We will be traveling for the holidays, too. Good luck and let me know if I missed your questions! D.