Teaching abroad is the dream of many travelers and there are two main paths to landing the gig. You can secure a job while stateside or you can find a job when you land in-country. Both of their advantages and disadvantages.
Craigslist and other online sites often have job listings for English teaching positions throughout Asia, often in South Korea, China and Taiwan. Some of these are legitimate companies, but some are not. The responsibility lies with the consumer (you!) to research their business practices and histories to decide if they are a company that you can respect and trust. It's a good idea to check out other sites, like Dave's ESL Cafe, to find out more information.
Finding a job while you're still at home can sometimes have the benefit of including air travel costs, visa fees and housing covered by the company hiring you. They will often take care of those details that are hard to do before you arrive (like finding an apartment) and take the worry of being about to find a job away. The trade-off is that companies that provide these benefits almost always requires a commitment of at least one year, sometimes two, to teach for them. That can be a disadvantage if you are not looking for a long-term job or if you are not sure you will like the country/culture you will be living in. Such a commitment is best thought about and not rushed into.
Besides not liking the country as much as you may have hoped, signing a teaching contract before you land puts you at the disadvantage of not having much, if any, control over where you live and where or how you teach. The housing may be less than satisfactory. You may find that you are required to teach more classes than you had envisioned or use texts that are not up to par.
Some companies require a payment for a position or placement at their schools. Sometimes this is legitimate and the courses are run by a non-profit for very low costs to local citizens. Other times it is simply a way for the company to make more money.
The other way to find a job is to look for one when you arrive in-country. This is for the brave and can be quite beneficial. You get a chance to check out the schools, meet other teachers and decide whether or not that city or area is best for you and your situation.
Teaching positions at universities and private language schools pay the best and competition for them is fierce. There are a great many people who teach English as a second language for a career and their resume may win those jobs over you every time, but there is no harm in trying.
Though in some countries it is not required, a TESOL or TEFL certificate is really great to have, both for the teacher and the students. Simply because one speaks English doesn't mean he or she can teach about the past imperfect tense or understands teaching methology. The courses are not prohibitively expensive and will make you a better candidate for teaching.
Once you've decided if you'll find a job here or there and are on your way to earning a TEFL certificate, it's time to choose where to go. You might be curious about Balinese culture or always wanted to visit China. Maybe you're looking to work a lot, then travel for a while. Do you like urban areas or do you want to live in the countryside?
Teaching positions abound throughout Asia. What you want from the experience and what you can give to your students will make all the difference as to where and how you teach. I taught children in an orphanage and later taught at a university. Each had its pros and cons, but it was wonderful experience, one which I wish could have lasted longer. The students are eager to learn and develop a friendship with their teachers. Respect their need to learn and the time they are investing as well as learning yourself about their language and culture.
Teaching English abroad can be a dream job, if you put some effort into finding the right fit for you.