I thought I'd add my two cents. Reason being, is because I work at UPS
My job is the person that sorts all of the boxes that are unloaded out of the trucks.
Truth: write the words "fragile, handle with care" all over it, and we'll still never pay attention to it. We see the label and zip code and we put it on the belt it's suppose to be on....sorry
It's already been covered how to pretty much properly package it. Whoever said just box up the guitar case, is an idiot

without any other type of stuffing, it will cause the weight of the case to shift inside the box. On the truck driving, it will move. When we put it on to the belt, the shifting weight may make us lose control over the box... potential damage.
IF you ship it by itself, bubble wrap it and peanut it in a box (who ever said peanuts don't get covered by UPS is also wrong, if something you did didn't get covered, it's because of something else) If you can, put that box into another larger box for safety. stuffing it as well.
If it's in the case, pack it with peanuts in a box. one should honestly be fine
No matter how you ship it.. make sure you have about 3-4inches of stuffing around your instrument..
USE A GOOD BOX!!!!!!!!!
USE LOTS OF TAPE!!!!!!!!!!!!
Tape the crap out of your box
single slice of tape down the top and bottom crack is no good for heavy boxes.
If you tape the opening that goes all the way down the middle.. tape the left and right side of it as well.. do that whereEVER you tape.
that's all..