Keep up with foreign affairs. Once you've found the personnel contact, you will most likely be asked to send a resume. Also, don't be discouraged if they don't call you back. Hiring for missions depends upon unpredictable funding. Check weekly on the status of the hiring.
Timing is everything.
The decision to begin deployment of staff may be made with as little as 24 hours notice, and a government worker won't have the time to search diligently through a stack of 500 resumes. Training will be invaluable, especially if this is your first international mission. In areas that are conflict-ridden, tense, or politically hostile to Americans, take appropriate precautions. Ask about the security situation in-country. Ask about evacuation procedures.