Currently my university does not offer any MOOCs. I am interested in creating one. How should I go about it? Does my university need to sign an agreement with one of the providers such as Coursera or can I approach them independently?
As far as I know, you don't need to have a signed deal with e.g, Coursera. You can do it independently. For example, the University of Helsinki has started offering some MOOCs, but they are not listed in the aforementioned provider.
One good approach would be to follow the line of Khan Academy, maybe it seems rather simplistic, but it can bring good results. One piece of general advice that I can give is to focus on quality instead of quantity. Just a couple of well-made online courses, with lecturers that have experience in the topics, is enough. Also pay attention to the evaluation tools that your site will have, that is crucial for its success and interaction with the prospective students.
Good luck in your idea!