Okay, I'm going to be basic, since I think that's what you're asking for.
Arrive at the airport. If you're driving yourselves, there are signs to long-term parking and the lot is divided by which airline you're flying (so you can enter the airport relatively close to your check-in place. You can park where ever, you'll just have to walk further if you don't park in your airline's area). If someone's driving you or you're taking a cab, it will pull up at Departures and let you out. Some airlines have curb-side check in. We always do online check in before we leave the house, up to 24 hours in advance. As someone mentioned, if you're checking luggage, in can be cheaper to pay that fee online.
Go to the Delta counter and give them your checked luggage. Then go to the security line. If you're flying out of B'ham it wil be really short. If you're flying out of Atlanta, it will be really long.
While you're in the line, have your boarding pass and ID ready. Take off your shoes and empty your pockets. We put everything from our pockets into my purse so we don't have a bunch of loose stuff to gather on the other side of the screeners. Have your 3-1-1 bag out. This is the 1 quart ziploc bag with your liquids and gels. This means ANYTHING liquid or "squishy", from shampoo to toothpaste. Liquid make-up goes in the bag. Powders do not. You are each allowed one 3-1-1 bag.
Put your shoes, laptop, 3-1-1 bag, etc into a bin and send it through the x-ray machine. Your carry-on will also go on the conveyor belt and go through. Batteries can look like bullets (especially if you have the super-duper pack of 60 AAs from Sam's. Ahem) but you can bring them. You walk through the scanner and reclaim your stuff on the other side. If they see anything odd in your bag, they will open and inspect it. You can watch, but not help them open it.
Then you just walk to your gate and wait for boarding.
I am another big fan of bringing more food than I think I'll actually need for the flight, and you can fill up empty water bottles after you pass through security. I wouldn't get on a plane these days without water.
Have a great trip! Despite all the frustrating rules these days, I still love to fly.
