You must be married to a Korean citizen, or a person with permanent residence in Korea (residing on an F-5 visa) to be eligible for a Korean F-2 visa. The Korean citizen may reside outside of Korea at the time of the marriage. The visa is also issued to some other categories, like refugees or employees of foreign governments who gain permanent residency.
The application should be done in person at the embassy or consulate of South Korea, but in certain conditions, can be done by an agent of the applicant. That may be the Korean spouse, but only if they were married during their stay in Korea, the Korean being older or younger than their spouse by 10 years or more, if either party was divorced within the past year and getting remarried, and those that got married by paperwork while the Korean spouse was still in Korea. In that case, the application can be done at the local immigration office or branch office in Korea, which can be found on the Korea Immigration Service website (hikorea.go.kr).
To apply for a Korean F-2 visa, the applicant needs to submit his passport, a photograph, an application for Visa Issuance or an application for Recognition of Visa Issuance, a document that proves the family relation (for instance a marriage certificate, a copy of family register or other documents verifying the marital relations). In addition, a document that proves the financial capability of the applicant and a reference for the spouse with Korean nationality is required. A fee of the equivalent of US$50 for the visa issuance was required at the time of publication.
Like most visas, the F-2 visa is granted for a specific duration of time only. Typically, it is initially granted for 90 days and then the applicant has to extend the visa. This is done at the local immigration office or branch office.
Those with an F-2 visa have the permission to work in Korea, but there may be other conditions for getting employment, such as having a valid university degree. These are not part of the visa conditions, however.