Rote memorization would probably be the simplest way of learning a new alphabet. Take some flashcards, write the character on the front, sound on the back, and then drill yourself until it’s branded into your memory. I tried this with the Japanese syllabaries and it worked. I tried it with Hangeul and failed miserably. No matter how many times I went through it, I would get ㅏ and ㅓmixed up, ㅗ and ㅜ mixed up and, sometimes, if the cards flipped directions as I shuffled them, I would get all four mixed up with each other. With Hiragana/Katakana I could make a sort of visual-auditory connection because the letters looked so different but Korean was too difficult. So, I ended up learning Hangeul in a weird, roundabout, organic kind of way without really TRYING to learn it through rote memorization.
That’s a question I get a lot these days, especially at graduate school interviews. Why Korean? I have no family ties to Korea, I don’t live in a place populated by a lot of Koreans (and those who are Korean prefer to communicate in English), and I don’t plan on visiting or living in Korea any time soon. Sure, there are K-dramas and K-pop which I love and obsess over 26 hours a day but that’s not the reason I started learning Korean. So what was it exactly? I’m not even sure I know myself.