This site provides Korean typing practice. It is good for beginners as you can learn to type the words at your own pace. The keys highlighted in blue are the ones being practiced.
Click 자리연습 if you want to practice typing the key. Click 단어연습 if you want to practice typing a proper word. This site seems to ONLY WORK ON INTERNET EXPLORER. ㅜㅜ Click image to go to site. You would need to add Korean fonts function to your keyboard.
Once, you have mastered the key positions, you can advance to simple words, phrases and sentences.
For mac-friendly typing practice, there's 타자왕 (Typing King) seen here above.
엔젤타자왕 (Angel Typing King) is a game that is found in junior naver, which means that it's actually designed for kids. But this is a fun game for advanced korean typist. You have to type in a limited time and it is not easy, but surely fun.