It's pretty simple. Just give yourself a little extra time...I've been through Dallas, Seattle and Atlanta; some times are quick others a little slower.
I use a small Stormcase and put it in my checked luggage bag. Typcially a Glock 26 with a few magazines and a plastic ammo case with 50 rounds of my my defense ammo.
I do tag the outside of my case with my name (and Army rank to look a little more "official") along with my cell phone number and email address. This is just in case they need to contact you for any reason.
I've had some open the gun case to inspect and I've had others just wipe the outside for residue testing. I've had a couple actually inspect the firearm to make sure it's unloaded and I've had others just ask me. To this extent, I pack a few long, bright colored zip ties and secure them through the barrel so it's easy to see it's unloaded.
Also, if your pistol case is inside your checked luggage, make sure it's sitting at the top and easy to access. They will still rifle through your checked luggage, but it's easier to keep your packed luggage from getting all messed up.
All my flights were point to point. It's good to know if your flight travels through a non-gun friendly state, but as mentioned, as long as you don't take control of your luggage you're safe. I can't confirm, but I've been told that if you were accidentally a lay-over in gun-restrictive state, the airlines can maintain control until your flight is rescheduled...you just won't have access to your checked-in luggage. You would also have to make sure you engage the airlines before getting your luggage dumped on you. Best to avoid those airports/states if possible!
ROCK6