I learned it by: ka ki ku ke ko sa shi su se so ha hi hu he go... etc... and how they're grouped visually. And by: ka na da ra ma ba sa, ah ja cha ka ta pa ha.. Haha. (:

For the consonants I think learning the names of them (much like we do with the English alphabet) is very useful. ㄱ- giyeok ㄴ- nieun ㄷ- digeut ㄹ- rieul ㅁ- mieum ㅂ- bieup ㅅ- siot ㅇ- ieung ㅈ- jieut ㅊ- chieut ㅋ- kieuk ㅌ- tieut ㅍ- pieup ㅎ- hieut I recommend this because when you pronounce each letter it will give you a clue to the intial sound and ending sound of each letter (except ㅎ- hieut - as there is no "t" sound when ㅎ is the final sound of a word). Example: when "ㅈ - jieut" is the final sound of a group of letters, like in 찾다 - it sounds like ㅊ("ch") + 아 ("ah") + ㅈ ("t") + ㄷ("d") + 아 ("ah") = chat-da NOT chaj-da. So saying it as jieut lets us know that "j" is the initial sound and "t" is the final sound.

For the next part, keep in mind the DARK and BRIGHT sounds. Other DARK vowels include: 여, 유, 에, 예, 워, 위, 웨. Other BRIGHT vowels include: 야, 요, 애, 얘, 와, 왜, 외. DARK sounds are combined with other DARK sounds, e.g. 우+어 = 워 / 우+이 = 위 / 우+에 = 웨 / 으+이 = 의 / etc. BRIGHT sounds are combined with BRIGHT sounds, e.g. 오+아 = 와 / 오+이=외 / 오+애 = 왜 / etc.

The way that I learned was that there are BRIGHT and DARK vowel sounds in Korean. 오 & 아 are BRIGHT and 어 & 우 are DARK. (으 & 이 can also be placed with the DARK sounds.) What does this mean? You have to use your imagination for the next part. The BRIGHT sounds are similar to when the SUN is the brightest 오 (sunrise) and (it then travels from the east) 아. Then the DARK sounds come in, 어 (going west) and 우 (sunset). Well, if you imagine that with the BRIGHT sounds, your mouth is more open and wide, and with the DARK sounds, your mouth is narrower and tighter. Try 아 vs 어 and you'll see that your mouth will be wider for the BRIGHT sounds and narrower for the DARK sounds and the same for 오 vs 우. Okay, so that is the basic part.

On YouTube there is a video called "Learn Korean: Hangul Rap" that helped me learn the vowels and consonants. At first I thought it was a little goofy, but it's actually VERY helpful. Just type in Hangul rap and it should be the first video that shows up. :) Hope that helps!