Language Specialist

If you want to be a simultaneous interpreter:
You have to go to a graduate level professional school and do a specific simultaneous interpretation degree. Your choices are the Hankuk University of Foreign Studies, Ewha and Chung-ang. Competition is about 20 to 1 and not all students graduate. Simultaneous interpretation is very difficult between the two languages (more so from Korean to English one reason for example, being that negatives come at the end of sentences in Korean. For example, ' ' becomes 'I don't like apples'. Notice where the negatives (in bold) come in the sentence. If you can do this well though, then congratulations, you're probably set for a high and stable income.
2. If you want to interpret for tourists ( )
This is a matter of getting a qualification by passing 1 written and 1 interview examinations. This is for interpretation for guiding tourists around, and requires knowledge of Korean cities and tourist spots, Korean history, tourism as an industry and tourism law. Level of language required is relatively low, and this is mainly for people whose first language is Korean.
3. If you don't want to do either of the above, amateur interpretation
You can sometimes find interpretation jobs without either of the above, but then it's a matter of you finding it for yourself. Even then, chances are that you'll only land jobs that pay little. To become a part of an interpretation company, you'll need certificates to prove your fluency in both, or that M.A. Degree I mentioned above. I would say the bare minimum would be TOPIK Level 6, if you're a native English speaker. There are many more Korean native speakers who are excellent at English than the other way around, and overall, especially in business, Korean is the language that requires more delicacy in translation (with register, tone, politeness etc. ). If Korean is your second language, then your chances are fairly slim. If neither Korean nor English is your first language, then don't bother. Interpretation (and translation) is the standard go-to part time job for the numerous Korean students who have studied abroad in an English speaking country, so the market, especially at a quasi-professional level, is pretty much saturated.