Well......I,ve just been through the process and it is a little complicated.
The visa that is most commonly used for teaching in Korea is the E-2. To obtain the E-2 requires a lot of hoops to jump through. Firstly..........if you have never had an E-2 visa before then you will be required to have an interview at the Korean consulate/embassy....in your HOME country. Can,t be done in Thailand, unless you are Thai.
You will also need to obtain your criminal records check which must be no older than 6 months. This then needs to be APOSTILLED.
You will also require signed and SEALED transcripts of your degree. No exceptions. If the consulate has some doubts, they will ask you to sign a waiver form allowing them to contact your University directly.
You will also have to undergo a drugs test ( once in Korea ) although they no longer test for cannaboids.
ALWAYS ask for pictures and detailed description of the apartment being offered. Some of them are no bigger than shoeboxes.
ALWAYS ask to see a copy of the contract and go through it with a fine toothcomb.
Apart from those hurdles......yes you can make good money and easily save. My salary is 4 million won ( approx $4000 ) per month with a free 3 bed house and utilities paid for.
The jobs are out there.......just do your research first.