I've been gluten-free in Korea for about a year now, and it's tough. Especially if you'll be out with family and friends, dining out is a big issue. The best thing I can recommend is to get a restaurant card that lists your food allergies in Korean, to show to the waitstaff. One thing I have found, if it's possible to make accomodations, Korean restaurant owners are really happy to help.
Be really careful of red pepper paste- most of it has soy in it. And sadly, most Korean foods have red pepper paste in it. I think that kimchi chiggae (kimchi soup) is about your safest bet, or dubu kimchi (uncooked tofu and kimchi). Bibimbop is good without adding any red pepper paste, and some of the meats at galbi restaurants (Korean BBQ) don't have a marinade (the beef that's cut into smaller pieces is my best bet). There are also some great rice and sweet potato noodle dishes, but the sauces are always iffy.
This is sort of a vague description, but if I can help more send me a message! I think Korea is about the hardest place to be gluten-free, but it's a lovely country!