I suggest picking a country or general area you want to go to first. Then look up teaching programs for that area because generally speaking different programs different countries different requirements.
For example, JET doesnt want people who speak or have lived in Japan for too long, but want people with a college degree (doesnt really matter what). Other countries, however may want more fluency in the language, or a specific teaching degree.
I suggest Europe over Asia. Most people, even the die hard Japan-o-philes, tend to be miserable there, especially since they tend to send you to rual areas versus big cities. While Americans who go to Europe from my experience, experience less culture shock and the people there are more inclusive.