There are some very Korea specific, dedicated forums where you will probably find most most of the questions ether already answered or currently under discussion. Do you know how to use a search engine? There's one called Google, but there are a lot of others too. Try using search keywords like Korea TESOL TEFL forum
, not only will the result list the forums, it will also list all postings on the subject. Give it a try.
If you want to earn very good money as teachers abroad in Asia, you could also try Japan and Taiwan.
Probably more has been written on the subject of TESOL certification than any other EFL topic. You will find information on this very web board and many, many others. Use Google again to find out more and do heed all the warnings.
Your choice will hinge between on-line/distance courses and proper courses. On-line courses will provide a very good understanding of theory. Face-2-face courses will provide the role play and practice which is needed to become a really good performer. Mos better paying schools will want to see a TESOL certificate and 120 hour courses are the most readily accepted.
More very valuable general information on TESOL training is also on this external TESOL forum