Pick up basic words and phrases by getting a book for travelers in Korea. The advantage of these books is that they generally include vocabulary items, written in Korean and spelled out in English, organized by topic. One highly recommended resource is Berlitz's Korean phrasebook, which offers more than 2,000 words.
Obtain a beginning Korean textbook. You can either purchase your own or check your local library resources (ask for an interlibrary loan if no Korean materials are available at your local branch). Be sure to select a text with accompanying multimedia materials, so you can hear people speaking vocabulary items aloud. One of the best of these is Integrated Korean Beginning 1 by Hyo Sang Lee, et al. This textbook is accompanied by a complete and free audio course that is hosted by the University of Hawaii (see Resources below).
Use online vocabulary lists to learn basic Korean words. Korean Flashcards (see Resources below) offers both free and pay accounts that include flash cards as well as audio to enhance your reading, speaking and listening comprehension. The eLanguageSchool also offers good learning materials with audio.
Consider making use of the skills of a Korean tutor. You can ask targeted questions about the vocabulary you're interested in, have a chance to practice what you know and have your mistakes corrected on a one-on-one basis. You could also go to a Korean discussion group, which you might find in a town with a large Korean population or in many college towns.
Enroll in a beginning Korean class for more organized study. Teachers can present vocabulary and grammar in a logical fashion and address any issues you may have with learning the language. You will also benefit from the chance to learn Hangul, the Korean writing system.