Have a hard sided container you can lock and the cheapest little airline padlocks you can find at WalMart. Put the gun in the hardsided container, unloaded, and put a padlock on it, but do not lock it. Put the hard sided container in your suitcase. Put your ammo, still in the box in which it was purchased, inside the suitcase. Put another padlock on the suitcase.
Go to the TSA site and print out the information for checking in firearms. Keep it in a manila folder with your travel itinerary. Print out your airline's procedures as well (do not call and ask). These items should stay with your tickets, itinerary, rental car, hotel, and map information in the manila folder.
Bring your unlocked items to the check in counter. Do not bring it to the outside check in, or you will wait in line in vain. Upon reaching the counter, declare, "I have a firearm in my checked baggage to declare."
This works better than "I have a gun!"
Then take out the hardsided container (see why I said not to lock anything?). The airline person will ask if it is unloaded, which you will confirm. He will then hand you a red tag to sign, which you will put inside the hardsided container and close, locking the padlock. Then put this inside your suitcase and lock the other padlock.
Caveat: Last time I was at the airport, both the airport person and the TSA person made me put the tag outside the closed container, inside the luggage. I explained to them that this is not the way it has ever been done, and also my opinion of how retarded this method was (what would they do if I checked the hardsided container seperately?), but they insisted, so I figured it would not matter so long as I watched my luggage get locked up and put on the conveyor belt.
And so I did. Of course, I always do, and you will see why below.
The airline person will then direct you to the TSA with the luggage containing the firearm. You declare the firearm again. They will probably ask for your key. Do not let the key or your firearm out of your sight until the container and the suitcase are locked and you see them placed on the belt to go to the plane. In fact, I never relinquish control of the key, but offer to unlock the locks, if necessary. The same goes for combinations, if that sort of lock is chosen. Do not divulge the combination to anybody, no matter what.
This is where having the TSA regulations and instructions from the web site will come in handy, as I have had TSA and airline people try to take my key and take the weapon out of my sight. I always refuse and force them to follow their own instructions and regulations. Last time I flew the joker tried to get me to unlock the luggage and gun and walk away before he locked it back. I refused. Sure enough, he tried to put the gun in an unlocked portion of the luggage, and then deliberately ignored me the first two times I pointed this out to him. I got his attention on the third time by being a little more insistent, as the situation required, in spite of the fact that it drew a bit of embarassing attention to both me and him from the surrounding crowd.
I wonder if this is a side business for some of them? Providing firearms to ramp guys and getting a kickback?