The public calendar works only if the module
Network & Community is part of your pakage. If that is the case the application link "Events" has to be active (T
ools & Administration > Design & Layout > Application Links/Overview > Tab
Network & Community/Events).
By default only users with the role "Calendar User" and Portal Master of course are allowed to enter public events. But you can also allow this e.g. all of your members or only your Premium Members, by assigning the permission "calendar_create_public" to the corresponding user role (
Tools & Administration > Access Rights/Permissionss).