Obtain your U.S. Passport if you plan on living in Korea for less than 90 days as a tourist or on business.
Obtain a visa if you are staying for more than 90 days. All visa applications will require a valid U.S. Passport, a completed visa application, a 2" x 2" passport photo and a $45 fee in cash or money order made out to the Korean Consulate General.
Visit the Embassy of the Republic of Korea website at www.dynamic-korea.com/consulate_service/visa.php. Determine the type of visa you will need and procure the other necessary materials listed on the website, then mail your application to the embassy. Visas can also be obtained at the nearest Republic of Korea consulate.
Arrange for a place to live before you arrive in Korea, if possible. if you are moving there for a job, you and your employer will likely have already settled on housing arrangements.
Search online for rental housing on sites such as Justlanded.com and others that specialize in housing for foreigners.
Ensure that all monetary exchanges and reservations are backed up by paperwork.