Be sure to start by going through the Steps to Study Abroad  section of this website. It outlines the process and describes how study abroad works.
Also check the section on Major Advising Pages  to see if one has been created for your major already. If so, you’ll find some good tips on classes that can satisfy major or certificate requirements beyond earning elective credit towards graduation.
That being said, South Korea is an excellent choice for a study abroad destination if a student wants an academically rewarding and culturally enriching experience in Asia. The universities are top notch. The culture is a relaxed blend of Asian traditions and Western modernizations. And the largest advantage to students from the US is that many of the classes at Korean universities are taught in English. The academic environment on campus creates a comfortable base for exploring the rest of Korean culture and society.
There are essentially five paths to South Korea. Clicking the links below will take you to more detailed explanations of each and links to other websites that may be of more assistance.
Direct Enrollment : directly enrolling as a non-degree seeking student at a Korean university
Exchanges : pay UI tuition and fees to study at a Korean university
ISEP : a large network of universities that exchange students
Program Providers : companies working with universities to create themed study abroad experiences
Summer Schools : short-term summer programs sponsored by major Korean universities