Lars has it about right. You check in and tell them you have firearm. They tag your bags/case and you will be sent to another window where it will be inspected. You hand them the key, they inspect, lock back up and give the key back to you.

When you arrive you will have to pick it up at a special room. Usually the same place you get oversized bags, carseats or report missing bags. At least that's the case everywhere I have flown except SFO. Once I flew there my shotgun came out on the regular baggage claim. You should have seen the faces of all those hippies when I grabbed an obvious gun case from the baggage claim! Ha!