You need to pack it the same way you would for shipping. That means you have to pack something around the guitar to keep it from moving around in the case. Pieces of high-density foam work well for this. You will aslo need to protect the finish from bruising, by wrapping the guitar in soft cloth, like a fluffy towel.

Do NOT slack off the strings. The neck is happiest when it has balanced tension on it from the strings and the truss rod. If there is a trem bridge, pack a foam frame around it so that there can be no pressure placed on it. This will help to prevent changes in string tension during the trip.

If you care about the appearance of the outside of the case, you should cut some pieces of 1/8" (3 mm) masonite to cover the outside with. This stuff is good for protecting against scuffing.

Call the airline about how to arrange to check-in your guitar at the loading gate. That way, it will be put on board just before departure, and it will be one of the first things off-loaded at the destination. Items given this treatment tend to be handled more carefully than the usual baggage-gorilla stunts that happen for the rest of the load-in.