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for public schools, there are three main programs, base your choice of them on where you want to live.
In Seoul contact SMOE: http://etis.sen.go.kr/
The province surrounding Seoul Gyonggi-do has their own program called GEPIK.http://cge.ken.go.kr/
If you wanna work way out in the boondocks, do EPIK: http://epik.niied.go.kr/
If you're more adventurous you can go the hagwon route.
HOGWONS JNiki Battle
Hagwons are really funny. What no one tells you is that contracts are more like guidelines, so Hagwons can always be difficult. But I would recommend looking into CDI (Chung Dahm Institute), SLP, Yes Yung Do, or Poly School. They are more like big corporations and very familiar with hiring foreigners. They are used to working with foreigners, so they expect the issues that we bring over here, i.e. racism. They will work you though. No real holiday packages with these schools.