If you are coming to Korea with only one person working, your wife or husband ( Legally married couple) can get F3 visa ( Spouse Visa). You can apply for it in your home country or in Korea. But please check first if your country is visa exempting country or not when entering to Korea.
1) Passport ( Applying for spouse visa)
2) Passport size photo
3)Copy of marriage certificate with translation into Korean
4) Copy of front and back side of alien card ( Having E2visa)
5)Working Proving letter ( Person Having E2 visa)
6) Visa Fee ( 60thousands won)
7)Application form ( you can get in the immigration)
Processing time: 2 weeks
Person who applying for spouse visa needs to go in person and apply.