Head to your library to search for free Korean learning resources; if these are not available at your local branch, ask for an interlibrary loan. One of the best resources for English speakers beginning to study Korean is "Integrated Korean"; the first volume is by Hyo Sang Lee, et al. This book comes with excellent audio resources to help students work on listening comprehension and language production skills; these files are available on accompanying CDs or on a site hosted by the University of Hawaii.
Sogang University provides very thorough online courses for Korean, all at no cost. Beginning with cultural information and an overview of the language and taking students all the way through third-level intermediate Korean, this site offers step-by-step instruction, interactive resources and prose explanations.
KBS World Radio offers introductory lessons on language basics, including the writing system, and another set of lessons that feature animated dialogues in real-life situations. These are well-translated and feature audio in Korean and English.
Learn Korean Language is one of the most user-friendly resources for English speakers learning Korean. Its advice on learning Hangul, the writing system, is particularly helpful, and there is information about configuring your computer to type in and recognize Hangul.
My Language Exchange connects speakers of different native languages so they can share language knowledge. You can improve your accent and work on writing with a partner from Korea while you help her work on her English.