Depends greatly on your learning curve. Also depends what you mean by learn, do you mean simple phrases or fluent speaking of it? It would probably take at least 2 - 4 years to be decent in the language and have a basic understanding. Try finding a class to help you learn.
Korean isn't especially hard for Americans to learn because the written language is phonetic. But they use a lot of Chinese words and characters, and those can be tough to learn. Expect it to take about 3 months to learn and use the very basic parts of the language, 6 months to chit-chat a little, and a year to understand more complex use of the language. A face-to-face class with a teacher and students would probably be fastest because you can get immediate correction and feedback on speaking Korean.