And just like QWERTY is way more popular than DVORAK, 2-bulsik is a lot more widely used than 3-bulsik. 2-bulsik is more user friendly whereas 3-bulsik is for power users. Unless typing Korean is your full day job, you would be happy with 2-bulsik.
2-bulsik is simulated on this website.
Left hand for consonants and right hand for vowels.
You know Korean consonants can be placed as the beginning sound of the letter, or the ending sound of the letter. Using 2-bulsik, you just keep pressing the consonants and vowels of the words and the input system will automatically figure out whether to make the consonant as ending sound of current letter or beginning sound of the next letter. For example,
You type ㄱ + ㅏ => you get 가
You type ㄱ + ㅏ + ㄱ => you get 각
You type ㄱ + ㅏ + ㄱ + ㅏ => you get 가가
You type ㄱ + ㅏ + ㄱ + ㄱ + ㅏ => you get 각가
* You do Shift + ㄱ to type ㄲ.
The difference with 3-bulsik is that it assigns different keys for the beginning consonant and ending consonant. It increases the number of keys we need to memorize, but you might be able to type a little bit faster since you don't have bottleneck on your left hand. Think about typing 각각각각각 in 2-bulsik: 10 times R key and 5 times K key.
Still, 2 bulsik is not bad at all. Personally I can type in both layouts.