Answer:
My experience is exclusively based in Latin America, so bear this in mind.
One very popular way to work abroad is to teach English. If you are a native speaker, this has the added benefit that you are using a natural talent that you have for the native population's benefit, and you are not essentially replacing a local that could do the same job as you.
If you're interested in teaching English and Latin America sounds like a good option, you might find my personal experiences interesting. I came to Latin America in January 2009 with the intention of teaching English, but I felt like I needed to get some kind of training first, partly in order to deliver quality lessons to the students I would be teaching.
As a result, I got a TEFL certificate at a place called the Dunham Institute in Mexico, and I recommend the course highly! It is 4 weeks and pretty intensive, but I needed every minute of it to prepare for my teaching it also helped smooth the cultural transition a bit spending a month in the same corner of the world for my training where I would be working and getting to know the way things functioned (very different to the UK!).
The training had a heavy focus on the practical (they had me teaching in class within a couple of days of starting) and even though it was hard I was a LOT better prepared to walk into a classroom afterward and start doing my thing. I wasn't perfect by any stretch, but my students got a much better teacher than if I would have tried to wing it.
The bit which is probably of greatest interest to you is a new program that the Institute are running now, where after the 4 weeks teacher training you are placed in a local state school to provide English lessons for the students for a month. This means you will be providing a high quality service to the community for which you have been properly trained, and you'll also be setting yourself up nicely for any future work teaching English (if that's what you decide you want to do) by getting experience to add to your training.
If this sounds interesting to you, you can have a look at the Institutes's website below in the Related Link.