DO NOT LOOSEN STRINGS COMPLETELY !!! Depending on guitar construction, Damage to neck may result. IF extreme low temps are anticipated, detune a couple of steps, but do not take all tension off of the neck.
Bubble wrap around neck and body to reduce movement within the case.
Get an oversized box and fill partially with packing peanuts. put guitar case inside and pack with peanuts to prevent case from moving.
Make sure signatures are required for delivery and tell the receipant to file a claim if there are any punctures to the shipping carton before accepting it.
Photograph before insertion. Insure, but don't expect the carrier's insurance to be very cooperative should you try to file a claim. That's why you need the photos.
Fed Ex always did well for the clients of mine. UPS, not so much.