Using LDAP group membership for project membership and management

I need some assistance understanding how to create project spaces, permissions whose membership is controlled by an LDAP group.  

I have followed the documentation, but am still missing some component.  We are evaluating this for a full offering of an on premise JIRA to all of Sandia National Laboratories.  It is critical that I solve this problem and get some guidance on best practices for creating protected project spaces.