I fly all the time with guns, both domestic and internationally.  Its easy and nothing to be stressed out about, especially if its domestic travel and its a standard hunting rifle.
- Have a good rifle case - like a Pelican or Americase. Make sure it really presses down hard on your gun and locks it in place inside the case.  It should leave a good indentation in the foam when you open it up!  Don't put anything in the case that is bulky that will cause your gun to not sandwich inside the case.  Make sure you have both a luggage tag on the handle and write your name on the case as well in ink.  I also put survey tape on the case so it easy to identify incase there are multiple guns on the plane (happens all the time going to Canada)
- Get a good combination pad lock (Masterlock) or two depending on your rifle case.  Don't use TSA approved locks.  The objective is that only you should be able to get into the case.  You don't want some TSA guy getting into your case without your presence.  I use combo locks so I don't have to fumble around looking for keys all the time.
-I usually take the bolt out of my gun.  If traveling internationally, I put on a trigger lock as well.
-I pack ammo separately and put in my luggage.  Must be in a box and not lose.  What I have been doing lately is putting my couple boxes of shells inside a locked hardside case inside my checked luggage which is also locked (with TSA approved lock).  Some of the international airlines are now requiring this, so I just do it whenever I fly.  But its not really that necessary on domestic flights.
-I usually get to the counter at least two hours before lift off time.  This gives plenty of time for check in and any TSA B.S. that you may have to do.  
-When you check in, you will have to signed a form to declare that you have a firearm and that its unloaded.  Its usually bright orange or white.  This paper will go inside your gun case before you check it in.  The clerk at the check in counter will give you the form
-Some airlines will request that you put a form in your checked luggage that has your ammo.
-After you check in, and they take your luggage, I usually hang around the TSA luggage security area.  They will usually come out and have you open up the case to inspect your firearm or swap it for explosives or whatever they do back there.  I always ask that they open it in my presence.  Usually not a problem.  After than, I go through security check and go to my gate.
-At your destination, the gun will usually come out on oversize belt, but I have also picked it up on the regular belt.  Depends on the airport.  Sometimes TSA will bring out and you have to show your ID and luggage tag to take ownership.  Again, depends on the airport.
This is what I have been doing and it works no problem.  I haven't been on a hunt in the last 4 years that hasn't required a plane trip.
Most important is a good bulletproof gun case.  I think luggage handlers drop and beat up gun cases on purposes.  My Americase looks like its been dropped off a cliff multiple times and is completely beat up.  But that is just cosmetic as I've yet to have issues with my scope being knocked off.  
Good luck, and don't sweat it...its easy