I travel with guns in checked luggage often. Here is how it goes when I do it. Check the airline rules on what they allow for guns and ammo. Most airlines only allow 11 pounds ammo domestic and international. Alaska allows 50 pounds domestic. Alliante only allows certain amounts of various types of ammo, sometimes much less than 11 pounds. United has no restrictions on what kind or how many guns you can fly with. NW restricts the number of rifles, handguns, machine guns and silencers you can have in the case.
Arrive at ticket counter, gun case unlocked and inform ticket agent that I have unloaded firearms in the gun case (or a gun case in the luggage). Fill out the orange "unloaded firearms" tag and put inside of the gun case, or the suitcase, then lock it. No ticket agent has ever touched a gun case or any luggage that has one of my guns in it, not even to weight it since the TSA took over. Declare any ammo you have in other suitcases. The ticket agent will most likely not examine it, but will ask if it is properly packaged (in ammo box or original container), just say yes. You do not have to explain.
The ticket agent will then call for someone to escort you to the TSA area or direct you to it. If you are lucky, TSA will examine the gun case (swabs and x-rays) while you watch. At some airports they do it in a secure area where you can not go. If it is the latter then it is best that you wait for 5-10 minutes to give them a chance to x-ray it and determine whether or not they want to open the case. They are required to make a reasonable attempt to locate you before picking or breaking off the locks to get into the case. Bring extra locks with you just in case you need them. They may ask you for registration forms if you are carrying silencers or machineguns. You are not required to show them, but the case might not make it on your plane before they decide to let them go if you do not show the forms.
When you get to your destination, you might find your gun case with the other luggage, or in the over-sized luggage area, or at the airline office at baggage claim where they might ask for ID before giving it to you. I usually discretely open the case and make sure no one replaced my guns with weights. I have done this while airport security was walking by and they had no objections. Best you do not take the guns out of the case while in the airport though. I use a small dolly when flying with my large rifle case with 60 plus pounds of guns.
I normally find a TSA notice of a luggage inspection whenever I travel domestic, sometimes when I travel international. I find my ammo containers are usually opened then resealed with TSA tape when I arrive at my destination. Keep small parts attached to the guns so TSA does not loose them when inspecting.
Ranb