I'm not some travel guru, but I went from being entirely terrfied of setting foot on a plane to being fairly used to it in the last year or so...
Been in/out of/through the following airports: Tampa, Houston Intercontinental, John Wayne (Santa Ana), Chicago Midway, Newark, Atlanta, and London Gatwick.
Tampa, my home airport, is by far the nicest, cleanest, and better organized and staffed. Different airports are like night and day in all terms - even in policy and procedure.
I can get through security on an international flight at Tampa in under 20mins, and it took me over an hour for domestic in Chicago.
Some advice..
Security:
Each airport is different. Vastly and suprisingly different. You'd think something with a federal mandate would have some uniformity. In general you'll have 3 checks to get through. You'll have to have your boarding pass verified at some point, you'll have your lugagge scanned by x-ray and checked for liquids/sharp objects/other contraban, and you'll have your shoes x-rayed.
How they choose to do that is entirely up to the airport. Tampa lets you into the main terminal to do anything you want without any checks, then wont let you goto the airside terminals without doing the check on the tickets. Once there, you do the shoes and carry-on bag x-ray, with a double check on your ticket/boarding pass.
Tampa has x-rays and "puffers" which stick you in a small plastic room box and blow air at you. They use them like 50% of the time. Your shoes come off, you throw your bag and any metal into the x-ray machien trays, take any laptops out of their bags, and run bags/shoes/laptop/belt all through the x-ray machine.
Shoeless, you go through x-ray and puffer and at that time should be holding your boarding pass and ID in hand. They may randomly decide to give you a pat-down.
At the other side, you reclaim everything and get redressed, there is sometimes seating.
At other airports, the above happens in any number of combinations. I've had to stand in seperate lines for x-ray of bags and then a whole new line to have my shoes x-rayed at a different checkpoint. Some want you to hold your ID and boarding info, others want it in the x-ray trays.
The worst of it was Gatwick where once i got to my gate for departure i was randomly selected (like every 3rd person) to get patted-down and have my bags open and visually inspected piece by piece, and had my shoes visually inspected too. I had to answer a bunch of questions too.
As far as i know, most US airports don't have gate-side checks. One you're at the airside area, you're fine.
Baggage:
Know thy size limit! Know exactly how big a carry-on can be and don't try to fudge it. Different airlines have different requirements. Also, most let you take a personal item AND a laptop(with case). So, that puts you with 3 bags to carry on the plane. Just remember the laptop has to be unpacked for x-ray - which can be cumbersome.
NEVER, NEVER, EVER put a laptop in checked luggage. Nor any other piece of valuable anything for that matter. It will get broken, stolen, or something. Checked lugagge falls off conveyors, magically dissapears, and generally gets treated poorly. My bag came off the plane soaking wet and i hadn't been to any airport where it was raining (they load checked bags uncovered during torrential downpours btw).
For clothing, dress for both indoor and outdoor conditions. Jetways (the little tunnel you walk to the plane) can be insanely hot or freezing cold. Then the plane itself can be cold during the flight or hot and humid when you're stuck waiting to take off for over an hour. Anything that is a "coat" will need to be removed for x-ray, but layered shirts wont.
About shoes, the some x-ray points have little paper booties you can wear, but just wear decent socks and don't go barefoot. You'll live. Wear comfortable shoes you can take on and off in seconds - you'll probably take them off to stretch a little during the flight too, so dont have stinky feet, buy some oder eaters.
Flight Booking General Stuff:
Be aware of your layover times. Only 45mins layover sounds wonderful - grab a bite to eat, got potty, walk around, board plane... but almost never works. Planes leave late all the time and then get stuck waiting to take off or in a queue to land. 3 hrs is long but the "safe" layover while about 2 hours seems to be the best middle ground. I would never take a 30min layover unless i didn't have to be somewhere that day.
Know other flights! Know which flights your chosen airline is flying that day to your destination. If you miss your layover or for some reason miss a flight you'll know where to run to in your panic. Try not to be on the last flight out of the day, because if something goes wrong, you're SOL until the next day.
Airlines can and do overbook or have changes in which aircraft is used (less or more seats) and bump people or beg them to stay with promises of vouchers and all sorts of other fun. An early flight can be overbooked or arrive too late for a layover, and voila your flight which was empty is now a mess. Just know that it can happen and pad some extra time and try not to be the last flight.
Other people crying hysterically about not making someone's funeral will make you feel horrible about getting to WDW at 11pm versus 7am the next morning, even if you will lose a hotel night.
Know your plane:
When you book, or actually, while booking and before accepting, know the plan you're going to be on. Visit Seatguru.com and read about the airline's version of that plane. Not every plane has audio system, tvs, or even a movie. Seatguru will also help you avoid cramped seats, ones which dont recline, and other problems like being too close to the bathroom.
Check the available seats before you buy the ticket. Nothing sucks worse then getting onto a plane, not being near each other, have no entertainment, and not being able to recline and having less footspace thanks to the first aid kit storage. Yes, they sell those seats for the same price as the others.
Use the computer:
Check in online. That's #1 important rules in not missing your flight. Lines for checking in are outrageously long. You bypass all that by checking in online, and then all you have to do is dump your bags. Most airlines have kiosks where you jsut scan your picket out ticket and then slap a tag on your bag and its off - and you're off to security and your plane. At London Gatwick I saw a 2hr line to check in. My online checked-in line to drop my bags just had 1 person standing infront of me.
Also, if you fly a discount airline that doesn't assign seats, checking in earlier online puts you in the first group to board the plane and select a seat. Normally you can check-in up to 24 hours in adavance for your whole departure or return.
Don't forget to check in for your return, again, usually up to 24 hours in advance.
Some airlines have you print out vouchers for headphones and will also sell them for $5 if you dont print the voucher, others only sell them, and ALL of them that have audio or entertainment systems will let you use your own headphones.
Food:
Continental wont stop feeding you, and even gives you sammiches on flights they specify as "no meal" or something similiar, Delta gives you snack machine food like granola bars and chips, while discount airlines like Southwest give you peanuts and bag of crackers shaped like little airplanes.
All of them will sell you vodka and bloody mary mix for $5 each.
If you're on a flight that serves a meal, be forewarned that further back you are the less chance you get of a choice (they run out of one or the other). It's usually "chicken or beef" which an be anything involving either meat from pesto to lasagna to panini. No, it's not always Italian.
Turbulence/Take Off/Landing:
The plane does move. It bounces, sometimes it jerks, and sometimes it feels a little like a roller coaster. You will not die and the plane is not crashing.
Take-off is a sudden acceleration, lots of noise, a little bit of bumpy runway surface, and then a "swoosh" moment sort of like a roller coaster and then you're in the air. After that it's just a matter of getting your ears to adjust. Bring gum.
Turbulence can happen at pretty much any time, but often happens as your rising to or coming down from crusing altiture and pretty much anytime you're going through clouds or stormy weather. It can be really mild like an annoying shaking every so often, or really horrible enough to make you nauseated. It will thankfully end though. If the seatbelt light comes on randomly during the flight, it means the captain anticipates turbulence. Just brace yourself and it'll be over soon. I find that not looking out the window during it tends to help, especially if it occurs during ascent/descent.
Landing is a whole new experience the first time. It's best described as a controlled crash. Don't let that freak you out. It's just that your plane heads toward the ground, often gets some wind gusts and can sway from side to side, has some shaking, and can either delicately hit the ground (rarely) or it just goes "thunk" and bounces a few times while they slam on the breaks and you feel the g-forces.
I've rolled, i've bounced, i've even had a very dramatic 'thunk' all of which i survived.
Well, i've typed an awful lot.. hope it's helpful. Hope i didn't forget anything.. Have fun, safe travels!