Paperwork and Personal Guidance?

I live in the U.S. and i'm planning on moving to Denmark in August 2014. I have never traveled anywhere out of the U.S. in my life and i'm clueless as far as applying for a Visa and all the other necessary forms i will need for my residence. I'm not even sure if i need to apply for all these forms right now but I've heard it takes time and i have a year to get all this figured out and the sooner the better! I'm going to live in Denmark until the year 2016, then I will then be moving back to the U.S with my Danish girlfriend. I'm unsure if i need a permanent residency or if there is a form of residency for 2 years of living in Denmark. I have a lot of unanswered questions and from what information I've been looking for on the internet I feel like I'm going in circles with all other searches I've found and I'm hoping I can get help to get on the straight path i need to be on. Thank you.