There are numerous agencies that hire teachers, but the key to getting a teaching job is to figure out what is your end goal. If your end goal is to be on the International School circuit, there are International schools all over the world--when you try to become an International School teacher--you have to get two additional certifications and normally, have to work five years at a lower tier school--teaching said curriculum--some International Schools are U.K system and some are USA system. I don't qualify for UK schools as I never taught in that systme. The second thing is then you go to Search Associates--registration 300 usd, apply to seminar 200 usd, and then, try get a job--nothing guaranteed. Most schools are two year contracts and then, you go see the world teaching in different countries with a rather good salary.
However, if your goal is to stay in one country. You go through an agency, just email blast the schools in that country, or find a job fair. In Thailand, there are government schools that don't really pay well and private schools that pay from not too well to very well. The government schools are the easiest jobs to get, but often, you have large class size and small salaries with no air conditioning. It's standard to provide lunch at schools and a housing allowance, some government schools have housing right next door.
What I did was just email blast every private school in Thailand, and was lucky enough to get a job interview by phone. Agencies are good but normally, the pay is medium. Job fairs are also good, but there is a lot of legwork.
In Asia, it's very common for them to ask you uncommon questions--how old are you? are you married? can we have a picture of you? The laws are not the same as USA so just realize this is what living in another country is all about.
read our article about interviews