To work in South Korea for the first time to teach English you will need to obtain an E2 visa from the consulate general of South Korea in a country outside of Korea.
This process will take about four weeks to complete; 2 weeks to process on the Korean side, and another 2 weeks to process in the country where you will pick up the visa. You can either visit your local Korean consulate in person or mail it in via express mail. Once your visa is ready, you can pick it up at the consulate or have your passport mailed back to you (you must provide a return envelope).