I have done my post graduation in sports medicine from the University of Glasgow. The pre-requisites for sports medicine usually are a bachelor's degree in medicine or an allied field like physiotherapy or personal training or coaching. However, an interest in sports is sufficent for many universities.
It involves different modules like cardiovascular-respiratory system in sports, sports injuries, drugs and supplements in sports, sports psychology, etc. At the end of each module, you will have to present a paper making use of the current literature, stressing your critical views on the subject; say for example for the module on cardiovascular system, I choose to write on sudden cardiovascular death in young footballers.
At the end of the year, you are expected to conduct a scientific study in your area of choice or expertise, for example Designing a new exercise protocol for post myocardial infarction patients or Improved shoulder conditioning for baseball pitchers.
If you are interested in the fitness field, it is a good idea to start publishing your ideas in print or online. Early recognition will stand you in good stead for future references, not to mention in securing a scholarship. Also, as compared to other fields, there is a lot of scope for research and new ideas in sports.
If you want to know more, get in touch with me at firstname.lastname@example.org