Go to Guitar Center or nearest music store and ask for a guitar box. You may have to pay $10 or something but it’s worth it to get a manufacturers shipping box.
If your guitar has a hard shell case, then make sure the guitar fits snug and does not slide around at all. If it does, then bubble wrap it wear there is space. Make sure the headstock cannot take a direct hit on any hard surface.
Wrap in bubble wrap or use styrofoam peanuts to fill any open space between the guitar case and the shipping box.
I usually turn the tuners a half turn to loosen just a hair of tension on the neck. I’m not sure that makes a difference, but it’s a habit.