Korean students are generally bright and motivated, which can make teaching English here fun. The Embassy’s webpage on teaching English in Korea is: https://kr.usembassy.gov/u-s-citizen-services/local-resources-of-u-s-citizens/teaching-in-korea/
You should carefully review the terms of your employment contract, especially with regard to working and living conditions. You will need an employment visa called E-2 (Teaching) visa from the Korean government. To get the E-2 visa, you submit with your application a criminal records check, health certificate, and U.S. diplomas. Depending on the job and other factors, it can take from one week to two months get your E2 visa. Within 90 days of arriving in Korea, you must register with Korean Immigration and obtain a residence certificate and re-entry permit.