I've only flown with instruments within the US, not internationally. Checking instruments is allowed, but often involves extra fees for large instruments.
That said, the first thing to do is call the airline, and ask their policy. Find out if they routinely allow you to carry it in the cabin (rare), or if you have to check it. And if you check it, do you have to pay any extra fees. And be aware that if anything happens to your guitar while it is checked, you are in for a big fight with the airline, and you will probably lose. Checking will usually get your instrument home with you safely, but it is your riskiest option. If you look at the United Breaks Guitars link that another user posted, you find out the attitude generally taken by airlines to damaged checked baggage: deny any responsibility. Your instrument will probably not be lost, damaged, or stolen in transit, but if it is, you have very little recourse under the law.
A good second option is to ship your instrument, insured, with a reputable shipper. Within the US, I've shipped my violin UPS, and ordered a few which were shipped the same way. If they lose or damage your instrument, and you can demonstrate that it was properly packaged, they will reimburse or replace it. You can find specific policies with individual shippers as to values allowed. Just be sure to follow their guidelines and take photos when you pack. For international travel, I would definitely use this option if I couldn't carry my instrument in the cabin.