I travel 3 weeks a month and check a firearm every trip. I exclusively fly Southwest. TSA and each airline have their own requirements as far as handling firearms in checked baggage. It is highly recommended to go to both of their websites to read the requirements. I fly mostly to the West Coast (California, Arizona, Nevada, and Utah). As far as airports and their procedures, Tulsa International is pretty easy. Only once have I had additional security screening and that was because they couldn't get into my suitcase (they couldn't open the TSA approved locks). Phoenix always has me go to a secondary screener, but they just swab the case for explosives and away I go. Burbank California I always get the second check. San Diego, drop and go. Las Vegas, they take my bag and advise me to wait 10 minutes at the end of a hallway, if no one comes out in 10 min I am free to go. Salt Lake City, no issues. Ontario (by far the nicest airport on the West Coast) does require secondary screening.
Here is my procedure for traveling with a firearm.
1. I place the unloaded firearm in a gun vault safe that is secured to the frame of my suitcase. This case is to be locked and not accessible by anyone but you. TSA can request your key to open it for inspection, however I have never had that happen.
2. Ammunition is packed in my suitcase in its original container. I usually carry 50 rounds of defensive ammo.
3. When I check in, I advise the ticketing agent that I need a "Firearms Declaration Card". They typically fill out most of it. I sign it and put my address and phone number on it. They then place it in my suitcase on top of the gun vault. Sometimes they tape it, most times they just place it in the case.
Overall, it is a pretty simple procedure. The only place that I would probably not travel with my firearm is to New York or New Jersey, however it will be a cold day in hell before I go back to the North East.
YMMV
Textbook perfect example. This post should be a sticky in itself.