give yourself plenty of time - they used to say 2 hrs international, 1 hr domestic, but stay on the safe side and give yourself 2 hrs for your first domestic flight, just in case. American airports are horrible places to be in. It's pretty self explanatory from curbside to boarding - you walk into airport, you redeem your boarding pass via ticket reservation number at desk or preferably self check-in machine, everybody cattle herds through a TSA security checkpoint bottleneck, and then you find the gate listed on your pass, and you wait til they call your boarding group.
Wear comfortable but respectable clothing. Expect to have to take off your shoes, your belt, and everything out of your pockets, as well as anything metal off your body for the TSA scan, so expect that and don't carry more than you need. If you need to carry suspicious shit like medicine, carry it in prescription labeled bottles, and in ziploc bags away from your other stuff. Try not to make a tangle of your electronic stuff because you gotta take that out for the scan as well. On the bright side, you can carry a bomb through a TSA checkpoint and it's likely they will miss it in the scanner because they are too busy challenging people on their shampoo and conditioner.
Pro tip, seriously, if you are nervous about this - either call AA on the phone now and see if you can upgrade to first class or business class, or get to the airport early, check in on the e-ticket machine with your credit card and AA ticket number, and they give you the option to bump up classes. It's $90 or 115, can't remember, and most AA domestic flights are short, but still, to not have to line up with the angry people in coach, and going through priority TSA and priority boarding, getting a drink or two on board so that you can sit back and enjoy your flight - that is priceless sometimes. $90 is not a lot in the world of air travel nowadays. Seriously, upgrade for the extra cost, tell them it's your first time flying and that you want a little special treatment - they will give it to you and you will feel much better. It's their job to make sure you're 100% safe and reasonably satisfied.