My perspective on how to obtain a job in a different country is very limited. One important thing is to be fluent in the language of the country to which you want to go. Given that, I have seen three general approaches:
1) Go the the foreign country for additional training. That has been the most common way for graduates in medicine to go to other countries, but also applies to graduate-level (e.g., Ph.D.) researchers in other fields.
2) Get a job with a multinational corporation and apply for the postings abroad.
3) Carve out your own niche. This probably applies mostly to the professions (e.g., medicine, law, university professors). As just one example, the son of a lawyer friend found himself in law school but was not too enthusiastic about following his father's path. He drove a cab in NY for awhile and became fluent in Japanese and some other languages. He developed a small immigration-law practice, moved to Japan, and became extremely successful in that practice.
John