It's the same as the UN or AP. You should get popups from time to time asking you to vote for a leader and what proposal you want to put forward if you are elected, and if it's working correctly. I have been a member of the Overcouncil and that seems to be working as intended.
I'm at work right now, so I can't look, but I believe if you go to the victories screen there is a place at the bottom of the page for resolutions and members. Those should tell you what options you have as far as resolutions and should also list the membership of the council(s).
I also seem to recall that unless there were X number of members you wouldn't start getting the popups for the councils. I could be wrong about this last part though.