I've flown many times from the National Capital area to Kansas City, the Carolinas, Texas,etc. Flying United, Southwest, Delta, American, and USairways. Never had to show papers/documents at all. I have my pistols in a locked case,and have that inside a regular luggage bag. Declare the guns at the counter,fill out a 3 by 5 card that goes INTO the case,and it's walked over to the TSA. I also use the TSA approved locks for my luggage. I don't want to run the risk of somebody getting a wild hair up their ass,and wanting to physically search my bags,and having to cut my locks.
One young TSA idiot wanted to pick one of my pistols up,I asked why,his supervisor agreed with me. Another time,I was asked if I was a LEO,and when I said no,the guy seem surprised,but had no more questions or comments.
Other then that in the past 5 years I've flown guns I've never had a problem. I would still call the airline and or visit their website to check for any changes in flying firearms before every flight. Years earlier there was no limit as to how many firearms you could fly with. Some airlines are now limiting how many guns you may fly with. Just do you homework before you walk up to the ticket counter and you'll be fine.