When I moved here for work, I picked an apartment less than a mile from the island.
Trisha and I took our kids there the summer we met.
So when it came time to plan the wedding, we decided to host it there. That's where the whole state-taking-over-from-the-city thing threw a wrench in our plans.
In prior years, the all of the facilities on the island could be booked starting on March 24 of that year. This is no longer the case. The city has finally taken down their Belle Isle page, two months after the shift from a city to state park, but in the last two months we've chased down threads of information about the various sites and finally have a comprehensive understanding of what to do.
*NOTE: As of April 2015, it appears that Shelters 1-7 are closed through the end of June. If you've got your heart set on one of those, you'll have to talk to the park office.*
For everything else, you've got to go to the Administration Office in the White House on Belle Isle and talk to the park staff, or call them at 313-628-2081. The State of Michigan has provided a rate sheet for everything including the Flynn Pavillion, Belle Isle Casino (not that kind of casino), the Conservatory, the fountain (you do have to have a permit to do a private photo shoot there), and ball fields for various sporting events.
They will also rent you to reserve space on the island for longer photo and video shoots, but the rates haven't been set from what I can tell.
Although I will say, based on our engagement shoot, no one is going to bother you if you're just walking around with a photographer and not asking anyone to accommodate you. (It is important to note that this shoot was done in April 2014, before the state took over official oversight of the park and before the typical park season begins in Michigan. Your mileage may vary. That said, I don't think it's unreasonable to go out there with a camera and take pictures.)