Fellowships could help you get your foot in the door. Fellowships that will pay for you to go overseas are a great starting point.
Some fellowships are work focused and some more academic in nature.
With a little creativity, you can tailor your time abroad so that you obtain the experience you need to launch a global career. It gives grants to US students, artists and other professionals for academic study or research in over 100 countries. The IIE homepage has very detailed information about the different types of programs offered. This program provides annual stipends and internships for 18 Americans to live and work in Asia. The program's purpose is to increase understanding of the region, and thus is intended for those individuals who do not have extensive experience in the area.