I've been flying with my guns on hunting trips for the past 22 years. Generally domestic flights are easier than international. I've flown out of Bozeman, Denver, Atlanta, Anchorage, and L.A. which was the worst as I had to pick up my gun case at the domestic terminal, then take it outside several blocks to the international terminal.
Reading through the previous 16 replies, there are many good points. I'll try to summarize and add my thoughts or experiences:
1. Check the airlines website on flying with them with firearms.
2. TSA rules specify that firearms must be in a hard sided locked case. DO NOT PUT TSA LOCKS ON THE FIREARMS CASE. If TSA wants in your case they will ask you to open it. I carry extra TSA locks and extra non TSA locks. I've flown with a hard plastic case, but like my Cabela's welded aluminum case better. I also remove the bolt from my rifle and put it in a plastic bag in my firearm case.
3. Some foreign countries require ammo to be in a separate locked container and NOT in your firearm case. I've always put my ammo in a separate TSA locked container in my checked bag. There is an 11 pound weight limit on ammo. NO ammo or gun part can be in your carry on bag. Ammo MUST be in fiber or plastic ammo boxes, and not loose or in clips or in ammo carriers that you wear on your belt.
4. Check your firearm at the counter where you check in for your flight. The agent will give you a firearm declaration slip that you sign and put INSIDE your firearm case right there. In Denver an airport employee will take your firearm case and you to TSA, then that employee will take your firearm to the baggage conveyor.
5. Book your firearm and baggage to your final major airline destination.
6. Gun cases are usually considered oversize baggage and are picked up at a different location than your other baggage. Sometimes they ask for your baggage claim stub and your I.D., other times your gun case is just sitting there.
7.. Give your self a little extra time both to check in your firearm and to pick it up.