Council requests are random events that occur while you are at your base. They are simple requests for aid in the form of money, equipment, or artifacts. Simply wait for your first council request, aquire the items if need be, and go to the situation room to complete the request.
Added 5/09/13:
Saint Gerbil adds:"Worth noting that that if you have the slingshot map the slingshot missions do not seem to count for this achievement."