The TSA website is very clear.
Do make sure you check the websites of the airline(s) you plan to fly. They may have some other specific guideline that you wouldn't normally think of. When I flew on one particular airline, they required that any ammunition be in the original packaging (which must also conform to TSA's guidelines).
Be calm, pleasant and patient. A couple of airline agents I dealt with were a little anxious. I don't think they were so anxious about the gun itself, but it seemed to me they didn't want to make a mistake.
One good piece of advice I read somewhere is to print out the guidelines from the TSA website and the airline and keep them handy in case there's a disagreement over specifics. I never needed it, but it was good to have.
@WOC, I have read more than one account of people carrying a firearm in luggage that also contained other valuables, such as photography equipment or jewelry as a method for making sure your other valuables don't get stolen.