Thank God I've never had to ship my guitars anywhere or fly with them but here is some info. I've gathered over the years from those who have.
Airlines have changed their rules concerning carry-ons which make it virtually impossible to carry your guitar on board with you when flying so it's best to be prepared.
Protect your guitar and case from damage.
Loosen your strings down all the way to remove the tension from the guitar. Remove the strap peg from the end of the guitar if it isn't glued in. It doesn't take much of a hit to split your guitar there. Put crumpled up newspaper or something around the headstock and neck area for support. A guitar's neck can break, (get whiplash), from rough handling even in the case.
Guitars with hard shell cases can be shipped safely without boxing but if your hard shell case is like one of mine, the finish chips or tears off pretty easy just putting it in the car and stuff so I would protect it anyway. Put it in a cardboard shipping carton. If you have trouble finding one, try to get one that a local music store is throwing away from a shipment of guitars that just came in. Add crushed newspaper, padding, etc. around all the surfaces of the case. If you only have a soft shell case, add a piece of plywood to the inside of the carton over the top and bottom of the case. Use fiberglass strapping tape to strap it all up good and tight.
Insure Insure Insure!
After a flight, check for damage at the baggage counter before leaving the airport.
Here's a tip from Ed Duemler...
After he takes care of the guitar inside the case as mentioned above, he...
As for flying - I always gate check the guitar. Carry it to the gate and get a check tag for it there. Then you set it down just before you get on the plane at the end of the walkway. They then Hand carry it to the baggage compartment and at the other end hand carry it back and when you get off, there it is just where you set it down. Much easier on the instrument and case. And they are happy to do it.
Here's a tip from Michelle...
I just wanted to say that I've recently taken my guitar on a plane and that they stored it in the coat compartment at the beginning of the flight. In front of business class they have this closet on airbus planes where they store your coats and stuff before the flight and they take guitars too. I knew that I could take it on the plane before. They might count it as your carryon when you get on.
By the way I love your site. Thanx, Michelle