Go to stores that are likely to have a box the size you need.
Are you shipping it with a case or gigbag?
A case solves the issue of protecting the guitar.
All you have to do next is to protect the case.
Take some large cardboard boxes apart and with strong, Post Office approved tape (packaging tape), cover the case and tape the pieces together.
A gigbag is partial protection for the guitar, but you need to build a box around that with some padding between the guitar and box.
Same thing if you are shipping it without any bag or case.
As far as strings go... you can leave them on. It would be no different than packing up your own guitar and flying across the country.
You definitely want to brace the neck and protect the tuning pegs.
Get small pieces of cardboard and fold them over with wadded up newsprint padding for the tuners.
Build up cardboard platforms for the neck and tape around them and the neck to keep them in place.
Protect the wood and strings from the tape with a bit of tissue paper or regular paper.
Remove the tremolo bar and secure it well within the box so the recipient can find it and not throw it out accidently.
Places to look for ready-made boxes that will fit a guitar?
Music stores
Office Supply stores that carry folding tables or other office furniture
The shipping and receiving departments of hospitals are generally FULL of cardboard due to the sheer amount of supplies they run through on a weekly basis. While these boxes will not be in a guitar shape, you can find some boxes with large surface areas with which to build your own box.
Padding...
Office supply places either sell or throw out peanuts and bubble wrap.
Check with someone who ships/receives glassware... like an antique dealer perhaps.
Take a look around your area to see what types of businesses you have there.
Anyone that ships or receives large or bulky or bulk-lot items might be a good source for packing supplies.
Remember... you don't have to pack it all pretty like it comes from the factory.
You want it to look okay, but protection is your most important issue.
Also, you may not want it to 'look' like a guitar from the outside of the package... for security reasons.
So a plain rectangular box is fine.
Be sure to weigh it with all the accessories, packing materials, and the guitar itself in order to get an accurate rate.
Be sure to understand the packaging requirements of the shipping agent you use.
You may need to meet size requirements.
The U.S.Postal Service has specific measurements you need to take to make sure they will accept it.
Have fun! 
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