FORTUNE — Dear Annie: I will graduate from college in the spring with a major in business (minor in economics), and I can already tell from the scarcity of corporate recruiters on campus that it’s going to be tough to get a job. I keep hearing and reading that some Asian and South American economies are growing much faster than ours, so I’m wondering, is the job market also booming in those places? Would I have a better chance of getting hired in some other country?

I spent my junior year in Kyoto, Japan, and have backpacked around Europe and Africa, and I think I could handle living in an unfamiliar culture. But I have no idea how to start looking. Should I just pick a fast-growing country, like maybe Brazil, and go? Or is there a better way? — Footloose

Dear Footloose: First, you’re right about the slowdown in campus recruiting: U.S. employers are being “cautious” in their hiring plans for the class of 2012, according to a new survey by the National Association of Colleges and Employers. After stepping up hiring of new grads by slightly more than 20% in 2011, companies plan hire an additional 9.5% this coming year (compared to hiring in 2011).

The best reason to think about an overseas job hunt, though, is not merely to escape the doldrums here at home. “In the decade ahead, it won’t matter where you work so much as how you work,” says Stacie Berdan, a veteran of management jobs spanning three continents and author of a new e-book, Go Global!: Launching an International Career Here or Abroad. “Anyone who wants to get ahead is going to have to think cross-culturally and understand how all the world’s economies are linked.”

Diane Gulyas, president of the $8 billion performance-polymers division of Dupont (DD), agrees. She notes that, at Dupont as at most big companies these days, nobody gets to senior management without some experience abroad.

“Roughly 75% of my sales are outside the U.S.,” says Gulyas. “So it’s frankly just not possible to have a U.S. career anymore. If you want to grow and expand into senior leadership, you’ve got to be thinking beyond the borders.”

How? Your idea of simply getting on a plane, while admirably adventurous, probably isn’t the best approach. “Twenty years ago, you could just pack a business suit and go. I did it myself,” says David Lange, a partner in consulting firm Pivot Leadership, whose global executive-development clients include American Express (AXP), Microsoft (MSFT), Pfizer (PFE), and Procter & Gamble (PG).

“Today, however, your best bet is to focus your job search on U.S.-based companies with extensive overseas operations. Let them know you want to get on a global career track. They will rotate you around to different countries,” he says.

For entry-level would-be globetrotters, a good place to start looking for openings with those employers is international career site Going Global. In addition to specific job listings, the site offers loads of useful information about which overseas job markets are hot.

Right now, for example, the United Arab Emirates (especially the capital city of Dubai) is “a favorite of multinational companies,” notes the site’s founder Mary Anne Thompson. Almost 4 million expats already live in the region, and 60% of employers there are actively recruiting managers (and management trainees) and professionals, many of them from the U.S.

What do international companies look for? “They will be especially interested in your language skills, either languages you already speak or your willingness and ability to learn quickly,” says David Lange.

The reason is that new grads often get assigned to work on projects with local employees who (unlike many managers and executives overseas) do not speak English. “For instance, I’m seeing many Asian-American grads, who learned Mandarin or Cantonese from their parents at home, being sent to Asia,” he says.

Berdan’s book Go Global! cites a recent poll showing that 52% of hiring managers ask candidates for multinational career paths whether they are fluent in more than one language. The other four questions most often asked: Why do you want to pursue an international career? (85% of interviewers pose this one); Give me an example of your cross-cultural competence (66%); Have you ever worked or interned abroad? (63%); Have you studied abroad? (42%).

Here’s another question: Do you have any experience at tutoring, training, or teaching? “Interviewers are going to want to know, not only what skills you bring, but whether you can transfer those skills to others,” says Diane Gulyas.

Among the hundreds of expats her company has on the ground in China, India, Brazil, Eastern Europe, and elsewhere, Gulyas explains, “we send people to fill specific talent gaps in marketing, manufacturing, and IT, but also with the understanding that they will pass those skills along [to local colleagues]. Not everyone is good at that.” If you are, you have an edge.

Bon voyage!

Talkback: Have you ever worked in a foreign country? How did you get the job? What did you find most challenging about it? Leave a comment below.