In May I spoke at a panel on global careers, part of a career event aimed at current graduate students called "Where do I go from Yale?". My notes:
1 - Our work is important. Even when conventional success is not immediate. The relevance of academic work is hard to measure and does not always correlate with credentials and achievements, nor with grants and publications. But the work is important, and this is why after graduate school you will find a place somewhere in the world to do your work.
2 - We know Yale as a 1st rate research university. Research in integral with an astonishingly successful education system. many institutions throughout the world are making an effort to learn from the American academic research model. The aspect of a liberal arts education is as important, and perhaps less well understood abroad.
(I am certain about Brazil, and I suspect this is true for many emerging scientific environments.) Understanding the connection between research and education at Yale will enhance your contribution - in academia or in business, abroad or in the US advising students from different places.
3 - Your work is good. Publish it. Go to conferences. Talk to people about what you do. Listen to people who say interesting things. People you meet at your first conferences are friends who will sustain you throughout your career.
(Personal aside: I learned about the job I still have in Brazil from my college buddy while I was at Yale. In the meantime, I worked for a couple of years at a Boston company I learned about through a graduate students of an academic friend.)
4 - Get your personal life in shape. Family life means different things to different people. Your need to find what works for you. To support and to be supported are especially important in international careers. Do it. Jobs, visas, languages, housing.... that will follow.
5 - Academia is becoming more international. It used to be that you could only find a job in a country where you "belonged"... or in the United States and select other few. Academic and business cultures everywhere are becoming more "American". You can work things out even if "you are not from there".