How I got a teaching job in Taiwan
First it started off with a flight to Taiwan. I took a TEFL course, bought a ticket and flew to Taiwan to find a job in Taichung. I did a little substitute teaching here and there for the first few months, did a few visa runs and then found my first job in Taiwan by going door to door to buxibans. I also looked on Tealit for a job.
How I got a job in Korea
For my third contract I flew to Korea to get a job in Busan. I started off on a tourist visa and then I found my job by looking on Koreabridge. I also found my fourth contracted job on that site too. Korea now requires a considerable amount of paperwork to get a job.
How I got a job teaching English in China
So the web is of course a good way to find a job in Asia, but if you're abroad already don't discard old school tactics such as pounding the pavement with a fistful of resumes. I have found jobs by both means. Some employers don't always know where to look for a teacher online, some haven't gotten around to doing it yet, and both parties prefer to meet in person than they do online.
The failure rate for this way could be pretty high. You could go to a lot of schools before you get a bite or find one that needs a teacher. But it's one more way to find a job. There are some places where that is pretty much the only tactic that's available. For example, if you wanted to find a job on the east coast of Taiwan that's how you would do it. Jobs are rarely posted on sites there. Meeting with the school is also another tactic for finding a good job.