Some organizations actually offer free Korean classes, and it’s also possible to participate in group or individual language exchange programmes. You can take private classes through a school or with an individual teacher.
Korean language teaching methods tend to focus on a lot of structure and grammar, and involve students memorizing a lot of material. If you are looking more for everyday spoken Korean to help you get by - ‘survival Korean’ - then make this clear from the outset.
Please follow this link for a list of Korean language schools:
It’s possible to teach yourself Korean although this requires motivation and discipline. Books and learning aids are available in shops all over Seoul, and there are many blogs and websites dedicated to the subject.