Going to the Beauty Shop
Okay, first things first. Unless you are totally fluent in Korean, then I advise bringing along a Korean friend or co-worker to translate for you. We're talking about your hair here. It doesn't grow fast enough to think you can get by with a few memorized phrases.

Something that really helps is if you have a picture of the cut, style, or color that you want. I found a tiny little beauty salon where the owner/only worker lives in the adjoining rooms. She can copy the hair cut in any picture I show her. I trust her completely in that department.

Coloring your hair, on the other hand, is dangerous business. I was blonde as a child, and for some idiotic reason that I can't remember now, I suddenly decided I wanted to be blonde again. (My hair is darkish brown with splashes of blonde and red.) So, armed with a picture and a translator, I marched myself into a well-known and popular beauty salon downtown. I think I was their first foreign customer.

Astarte (my friend/translator) entered into a deep conversation (argument?) with several people standing near my hair and already wielding scissors. I was sure things were under control. Four hours later, I emerged from the shop with what can only be described as nuclear orange hair. I started buying hats.

I don't advise getting your hair colored or permed here. Foreigners' hair IS different and not many stylists have had experience with it. They know what certain dyes will make black hair look like--they can't predict what they haven't tried before. Anyone with a positive coloring or perming experience, please email me so that I can say something nice here.