I'm seconding VC over here, Dave's ESL Cafe is a rockin' site when it comes to trying to find an English Teaching job ANYWHERE in the world. Used it myself a few times and got a few interviews and offers in Japan before I went with my current company. 3nodding
The other thing I'd recommend you checking out is EPIK. It's not private schools, but rather, it is the Korean equivalent to JET. Often when it comes to teaching abroad, it is easier to find alternate jobs once you are in the country and have some connections. So, don't despair if you end up having to accept a company you are less than happy with/isn't your ideal.
But also keep in mind that a number of places (especially in Japan at least) will only hire from abroad. So if you know for certain that there's only one or two places that you are willing to work for/at, then keep applying to those things. If getting to another country and experiencing life in a completely new and thrilling way is more important to you than who you work for, then don't worry too much about the details of who you work for [As long as you check to make sure they aren't shady!!! BE CAREFUL ABOUT THAT!].
Also take into account currency conversation rates + cost of living where ever you end up. If you have debt back home, you might need to check to make sure your salary that you'd be paid can manage the debt back home after you deal with daily living expenses. And make sure you have at least a 20% cushion. Conversation Rates can get really wacky depending on what's going on in the world. An example is that when I came to Japan, you got about 75 yen to the dollar. But then a few months back, when things in Japan were being messed around with to try to strengthen their hurting industries, it jumped to 120 yen to the dollar! Great for people who are coming to visit! Terrible for people who are living here and sending money home. gonk
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