Well, for starters don't freak out every time you see a Korean or Asian looking person, or when you hear someone talk in Korean. Treat them like humans. My boyfriend is Korean and we met when I attended one Korean language workshop. But I've never saw him as only his nationality - I saw him as a person and treated him like one. Even though I've been learning Korean for over 2 years I've never called him "oppa" because I do not have to - we do not live in Korea, we do not communicate in Korean 24/7 (since I am not that fluent yet), and it just doesn't feel right. No one ever thought I am a 'koreaboo' and I made many friends and travelled to Korea few times. If you do meet koreans or make friends with one of them - get to know them, do not just talk about your favourite group, idol, actor etc. I'm sure they will gladly answer your language questions or culture questions if you ask politely. If you are conscious and worried about that - it's a good start. I hope I helped you a bit.
It is okay to like songs and enjoy the TV shows etc. They won't blame you, probably it will make them happy. Of course you will meet some people who will think you are a koreaboo no matter what (some folks are extremely judgemental, just like everywhere in the world). Just try your best and don't be ashamed for what you like.
TLDR; Treat Koreans like any other person.