My friend, Claire Chen-Carter is an award-winning, Bay Area art director who started her career as an expat in Singapore. Here's her take on getting a job overseas...
These days getting a job 'there' is the same as getting a job "here"... network like crazy to obtain 1 or 2 good overseas contacts and have a decent portfolio. Then set time to fly there with your portfolio. Regarding the portfolio, having an online URL is a must so that it's a part of in your introductory email. And unless you are a CD level, don't have the delusion that some agency is going to buy your first-class ticket to fly there for interviews.
When i got my job outta VCU, email was getting popular but not as ubiquitous as it is now. I remember having to make long distance international calls from the US to try to set things up in Singapore. Now that is not necessary. Boy, do i sound like a dinosaur ("in my day, we had to dial a phone and know +011...")
Headhunters might be of more use, now, as everyone is more global.
As part of the networking (or just googling), one can find a headhunter contact in the target country. All the big recruitment firms here have offices there. they can give u a good overview of how the market is doing and hopefully give some good pointers.