I fly fairly frequently for work, but I’ve never had guts to check a handgun. My wife and I went to the Florida Keys for our 5th anniversary and much to her dismay I decided its time to make this happen. Turns out it’s pretty easy to do. I bought an orange pelican 1200 with pick and pluck ,and a set of matching master locks just big enough to fit through the lock points. Pick and pluck certainly does not look nice but it gets the job done.
Review your airlines policy, but for US air the firearm needs to be unloaded in a locked hard side case. Do NOT use a “TSA approved” lock, the firearm should only be accessible to you. Keep the key with you and place a spare in your carry on. This case can be put in your larger soft sided checked bag. I take the extra step of using a bike cable lock to lock the hard case to the soft luggage. While it wouldn’t take more than a few minutes and basic tools to get the cable off the bag, I would hope it would slow down a rogue airport employee looking to quickly make off with my Glock.
Ammo can be in the larger soft luggage bag, but must be in a manufactures case or similar. I carry buffalo bore their package is nice for reuse. Some airlines allow you to keep your ammo In the locked hard case others allow you to store ammo in a loaded magazine. I find it easier to keep it separate, as I generally fly US Airways. 
When you get to the airport go to the counter and tell them you would like to declare a firearm. If its busy you may want to ask where to go at the start of the line. At PHL I needed to go to the “special assistance line” at MIA I just went to the regular line. At the counter you will sign a little orange form declaring it is unloaded and unlock the case placing the tag inside. At PHL I was walked down to the end where my bag was handed off to TSA at MIA the X-ray is on a different level so I was told I’d be paged at the gate if there was a problem (there were no problems).
At your final destination you’ll claim your bag as normal from the belt so don’t stop for 6 beers after your flight lest your Glock becomes property of one of the homeless that roam PHL. Make sure you check the state laws of your destination before you fly with a gun and avoid NJ and NY, It is also a good practice to review the airline polices. I have flown, US air, United, and Delta in this manner.
