I am thinking about applying for a LLM program when I am done with my law degree in Norway. I am wondering about the recommendation letters one should have in ones application. It says that it should be from one of your professors at school. But the way law is taught here, us students don't interact that much with the professors, we mostly just listen to them in lectures. Thus I have not developed any kind of familiar relation with any of the professors I've had. Won't that make it difficult to get someone to write me a recommendation letter, when they don't "know" me? Or have I misunderstood how this works?

It's truly difficult to have some detailed recommendation letters in such case. Do you have to write a graduation thesis in Norway? If so, you should try to ask the supervisor of the thesis, who is supposed to interact with you relatively frequently.

I have to write a masters degree paper, I guess that would be the equivalent of a graduation thesis. I will have a supervisor from the school, but I do not know how frequently I will be in contact with this person, and it will most likely not be a professor, but a faculty member at the university. I am not sure how I can go about to develop any kind of relation with one or more of the professors, so that they can eventually write me a recommandation letter. Any tips?

It sounds like you are studying in the univeristy, so you still have time to get familiar with your professors. It's worth a try.