See
here for the instructions in English and
here for them in Korean.
A couple things to note. The application process is different for English speakers and Korean speakers now. There’s a central website that you submit to for the Korean application whereas English speakers complete the applications forms and submit to the designated email address for your consulate. English speakers should check the website of their consulate as the specific procedures vary from consulate to consulate.
The US Embassy Korea also has very good information on its website.