Typing in Korean is relatively easy, each key on the keyboard corresponds to a jamo, and as jamos are entered the IME combines them into proper blocks. Double consonants are accessed by hitting the shift key. To insert the occasional hanjia character (Chinese character), it is typed phonetically in hangul and then a pop-up transforms it into hanjia.
However, it can be difficult to type in Korean on a QWERTY keyboard until you have memorized the location of all jamos. While learning to type in Korean it may be helpful to buy pre-printed, pre-cut jamo stickers to put on your keyboard's keys to remember which QWERTY keys correspond to which jamo. These are widely availble online, and are inexpensive.
Demonstration of Korean typing in Ubuntu. The IME works similarily in other operating systems.