L.S.
For work arrangements, we flew with our son every other week until he was about 1 year old. We travel a lot as a family, and it's been relatively stress free - we just make sure we're prepared for most things that can happen.
Mentally preparing for what you'll need to do, and logistics will help you prepare - You'll need to pack, go through security, navigate the airport, board the plane, and keep you & baby happy in a pretty confined space.
Here are our tips:
Packing: I recommend packing light for the plane ride itself. Take a snack, a bottle of water for yourself, and a magazine in case you're lucky & baby sleeps. Everything else should be your essentials: your wallet, phone, diapers, wipes, extra clothes, food for baby, a small blanket. In case you have a gate change, you'll be glad you have only a few things to carry. And getting through security & boarding will be easier. Check everything else that you won't need while you're in the airport or on the flight. If you haven't bought a seat, then check your carseat, and take a very simple stroller or carrier. Be really organized, and keep it simple - keep your liquids that have to be inspected by security to a minimum (breastmilk, hand sanitizer is about all you really need to carry on). Use ziplocks to pre-package a small diaper change kit to grab & go to the airplane lavatory.
Going through security: Give yourself a lot of time. Use the family lane if there is one. Being organized and packing light will help. One thing to note is that you'll have to carry your baby through the checkpoint, without a sling or carseat or stroller. So you need to unpack/repack your liquids, get your shoes off/on, get baby out/back into carseat/stroller/carrier all handsfree. It sounds silly, but practice it - I like to unpack my bag, get my shoes off with baby in the carseat, then put the carseat into the xray first, so it's the first thing to come out on the other side. Otherwise, you don't have anywhere to put baby down while you repack your stuff.
Navigating the airport: Don't waste a bunch of time shopping at the airport. Go to your gate early and camp out, preparing for your flight. Pay attention to gate change warnings or delays. Be ready to board ahead of time. When traveling with an infant, I like to board as early as possible, so you can set up your space with bottles, etc. Once he's a toddler, try to be the last to board, so you have extra time to run around near the gate before he has to be contained in his seat on the plane.
How to contain your child in flight: If you've purchased a seat for your son (preferable), bring your carseat with you onto the plane, and keep your son in the carseat as much as possible on the flight. If he's going as a free lap baby, be sure to have some kind of carrier so you can have both hands free, like a baby bjorn or an ergo or sling. You'll need this in case you need to get bottles out, get a snack, or go to the restroom yourself! Personally, I hate traveling with a stroller, unless I have lots of time in between flights, or I absolutely need it at my destination. Strollers get broken by baggage handlers, and it is always a pain to claim if you've gate checked it. Only bring it if you absolutely need it. It does make sense to bring it if you are using an infant carseat on the plane and you need it to help carry your carseat & stuff. If that's the case, be sure you can collapse it easily to check it at the gate. For your night flight, try to get a window seat, where you and your son can be cozy and just sleep. For your day flight, try to get an aisle seat so you can get up for diaper changes, and to walk around if you need to.
Feeding: Feed your baby during take off and landing so he can clear his ears. Get comfortable feeding your baby quickly. If you're breastfeeding, make sure you are comfortable using your blanket or a nursing cover, and whatever nursing top/bra you wear. If you're bottle feeding, be ready with lots of bottles for feeding. This is the easiest soother, so make sure you are comfortable to get set up without all of the extras you have at home (example: a boppy is pretty bulky to take on the plane, you won't be able to set baby down while you're getting out of your top, etc).
Diaper changing: Change your son right before boarding, so you are less likely to need to change multiple times on board. For changes on the plane, check seatguru.com ahead of time to see if your airplane has a changing table in the lavatory. Example, airbus 319 planes have them, but boeing 757s don't. This way, you'll be able to mentally prepare for diaper changing logistics. If you're plane doesn't have a changing table, bring a changing pad or blanket that you can put down on the seat in your row, or over the seat cover in the bathroom, or on the floor. (I've used all of these - airplanes are gross, so be sure to bring some hand sanitizer for your hands & baby's hands if they touch anything) In a small plastic bag, have a diaper, wipes, an extra set of jammies, and a changing pad. Since lavatories are so small, you won't want to take your whole diaper bag. Just take this small kit. Keep a kit ready in your seatback pocket. Carry 2 extra sets of clothes for your son (1 piece outfits are easiest) in case of messy diaper blowouts. Also, carry an extra shirt for yourself in case of bad spit up accidents.
Staying happy in flight: When you board the plane, spend a few minutes getting set up. Fill your seatback pocket with all of your emergency essentials: a set of pre-made bottles (breastmilk or formula), pacifier, diaper changing kit, and any toys your baby likes already. These things should be easy to grab in an instant, so you don't have to fumble around in your diaper bag while your baby is crying.
Overall, keep things in perspective: Your #1 responsibility is to you and your baby, NOT to the other people on your flight. Focusing on keeping you & baby safe, happy, fed, clean, calm is what you need to worry about. And 8 hours seems like a lot, but it will pass. Take a deep breath when things get tough, ask for help from flight attendants if you need it.