I WILL MAKE CORRECTIONS TO THIS FIRST POST AS I FIND MY OWN ERRORS.
CHECK BACK OCCASIONALLY FOR UPDATES.This is a new thread, in which I hope we can put together information about teaching in Korea. There are various opportunities, each with their own requirements.
Correct me if you know better, please, but I will attempt to roughly describe what I believe to be true regarding the subject.
MY CATEGORIES: (of Teachers, not Visas)
1. Military members here on an A3 visa
2. Dependents of Military here on an A3 visa
3. Other Foreign English Teachers from outside Korea.
4. Korean born English Teachers from outside Korea.
5. DODDS Teachers, hired for teaching on-post or on-base

I found a website that seems very informative, with seven pages of info on various visas, etc. Here it is:
http://www.teachkoreanz.com/terms/immigrat.htm
WOW! This is a must read site -on the left it has a "Survival in Korea" block that explains about Rubbish Pickup, Toilets and much more! Newcomers-Don't miss it! The site is a New Zeland Co. which hires teachers, and it has not been updated recently, but the local information is still interesting, accurate and mostly current.The Korean Immigration Bureau site mentioned on page 1 of that site is incorrect. Here is the corrected site:
http://www.immigration.go.kr/indeximmeng.html This site is not too reader friendly. Here is another I have not researched:
G4F(http://www.g4f.go.kr) stands for Government for Foreigners. This site provides information on investment, employment, housing and accommodation in cooperation with the Ministry of Commerce, Industry and Energy, Ministry of Labor and the Ministry of Justice. Here is another:
http://shc.seoul.go.kr/data/Doing/ch08.pdf It is in proper English, and has some good visa information.

Dr. Worm found that US Military folks can now have a second visa, allowing them to teach legally. Of course they must meet the education requirements of any institution where they may apply. I'm not aware that the Korean Government has yet set any standards for individual tutoring in student's homes. That is a convenient and lucrative way to make extra money, often just teaching conversation. I'm told that some A3 visa holders today teach conversation on the side. I'm not prepared to discuss the legality of doing that for pay at this time. The issue of paying taxes to Korea for money earned by teaching should be properly considered. I won't belabor the issue, but for new folks, the Korean government has only recently cracked down on English Language teachers who had presented fake degrees and credentials. Both Korean born and foreigners were exposed, fined, deported or jailed. For us, there is an issue of not being allowed to teach on an A3 visa, issued to Military and dependents. We will discuss this issue as we get educated ourselves. If you are a school teacher, or know the requirements or websites of certain Hagwons or Universities, please help us develop this forum.

I seem like you are using up much your physical stamina here forum.
You are too kindness everyone.
My dear adviser ! Take your time !

Oh thank you,student! But I am off today. and it is too hot to go out! If you think I am doing a good job, you may go to the top of my post and click on the weight and balance (Scale) next to the red triangle. That way you can
"add to my reputation" ,whatever that means.

Pardon me ? what do say me now ?
where I have to click ?
And, is it hot ? here is not hot. where are you now ?
Here is Korea !
last, I am not student ! you know.....

When you call me "adviser", I call you my English "student"!
The icon above the green dot in the upper right side of my post-
It is a 저 울 icon. Click on it. Then click below "Add to Reputation."

32 is hot in Seoul!

OK..! I got it now ! And I did it.
Btw, I think today Seoul is not hot.