I have only done it a couple of times, but it was not really that hard.
I flew Delta, and here is how it went:
Unload your gun, place it in a small hard sided case.
Keep your ammo in the original manufacturer's box, and place in case also.
Lock case. Do not use a TSA lock, use something with a unique key.
Place small hard case inside your suitcase.
Proceed to ticket counter.
Check in.
Declare firearm.
Ticket agent will have you open case, and put in an orange tag stating the gun is unloaded.
Ticket agent will then escort you to TSA person.
They will open case, look at gun, and ask if its unloaded.
They swab the case, I guess for explosives, and put swab in a machine.
Then they will bring case to you to re-apply lock. You keep the key.
Then they will put case back in suitcase, and put suitcase on conveyor belt.
Thats about it. I didnt get hasseled, but I was flying from a small airport in Georgia to Salt Lake City, and back. It didnt freak anyone in Georgia or Utah out, but if you are from some weird place like California or Massachussetts, it might I guess.