I think most people watching dramas are learning Korean. (The frustration of waiting for subtitles and/or how wrong some of them are will get to you sooner or later.) At the beginning, a couple of years ago, I tried actually learning Korean, like how you'd learn languages in school. But it was a lot of information to take in, and I wasn't one for slow learning. I had to absorb any new information as soon as I could, not giving my brain a chance to rest. And then I would proceed to confuse two or more rules and it would all be so overwhelming that I'd completely stop. So then I went back to the basics and thought I'd strengthen those.
Hanguel was pretty cool once it stuck. It was fun looking up words and actually being able to pronounce it. Some might think nothing of it, but it really is a huge step in the process of learning. If you know anything at all, be proud and keep going. (화이팅! xD) I can spell a few common words here and there, and I'm fairly good at spelling words I've never seen written before, with the occasional mistakes. (for example 업서 instead of 없어) But with practice, you'll be able to get it right.
Learning should be fun in my opinion, so I always try to play games and keep the atmosphere light. I like to look up any K-pop song's lyrics. Although they're not the best place to learn from (in lyrics, they can use any form of the word, and don't have to actually form sentences, so using them in daily life would be strange), they help keep things familiar. (I'm so happy that I understood 90% of a K.Will song the first time I heard it without even looking up the lyrics!)
Connecting words to your life is also another cool way to practice. Whatever you are doing right now, just ask yourself how you'd say that in Korean. (I think 쓰고있어요 is what I'm doing now haha.) And I definitely suggest learning with a partner or someone. You have to actually show your progress and using yourself as a judge of that won't really get you far. (Two of my friends are into Korean like I am, but they haven't learned the hangeul yet so I can't even practice with them. T_T) I'm up for a language partner any time. 어서 오세요~ :D