How Can HOA Owners Bring Community Issues to a Vote When the Board Says No?

This question was submitted by Mark of Florida

We'd like to explore ways for owners to bring popular issues to the board for consideration. Two examples:

1. Owners want to form a garden club and use a common area for gardening, but the board keeps denying it. What's the best way to let all owners vote on this?
   
   
   
2. Our bylaws don't allow full-year rentals, but 75-80% of owners are out of state or international and want that option. Beyond a written proposal, what steps can owners take to move this forward?