Korea has a leveraged economy. However, it is a country along with Hong Kong and Singapore that has developed tremendously in the past couple decades. During that time, the stock market has hardly moved. It is unlikely that they won't make new lows. If you look at a picture of Ben Bernanke, then you look at a picture of 20 leading businessmen in Asia who have been making money over the past 20 years, and ask yourself who you would rather give your money to?
How to invest in Korea depends on the individual investor. If you know nothing about Korea, then you should probably buy an ETF. If you are an analyst, then you might want to look at some Korean companies.