Start off your quest to learn Korean by purchasing a language course book or computer program that contains both an audio portion and visual portion. This will insure a quicker learning process as well as proper pronunciation of words. Text courses are nice, but it is easy to teach yourself the wrong way to pronounce specific letters. Likewise, if you only listen to an audio program you will be able to pick up the speech aspect of Korean, but it may prove difficult if you need to read text.
As you learn, do not progress to the next chapter until you have completely mastered the material of the current chapter. Advancing too early will only set you up for failure. The ultimate goal is to learn Korean, not finish the program quickly.
Once you have started to pick up some of the language, try watching a Korean movie. There are many available in the international section of video stores. Rent or buy a movie with subtitles--an English-dubbed version will defeat the purpose.
As you watch the movie you may find that you understand bits and phrases of what is said. After a while you may be able to piece together sentences without having the subtitles on.
Looking through Korean magazines and other large picture based literature (such as children books) will increase the level of exposure as well. The pictures may give away what the text says. You'll begin to understand a few words here and there and eventually you'll be able to make out what the article is about.
After you have mastered the basics of the language and feel somewhat confident with you skills, see if you can find someone available who speaks the language as well. Talking to someone who knows the language will help perfect your language and force you to think on your toes. This will quicken your response time and you may also learn the proper pronunciation of any words you were having trouble with.
It is extremely important that you continue practicing what you have learned. If you don't live where Korean is widely spoken, it will be easy to forget what you've learned. Have an occasional brush up lesson from your course or pop-in a Korean DVD. It is important to stay fresh to make sure you keep up your newly acquired Korean language skills.