Do you have a container showing on the module, since all the actions (Add Event, etc), only show if their is a module container. The Add Event button should appear on the module action menu, or to the left of the Month view, Week View, List view buttons at the bottom of the module. You will need to have the page in 'Edit' mode by selecting this raio button at the top of the page as well.

Note that event module editors can add new events, and edit their own, but cannot edit other users events. Only moderators can edit all events.

Cheers
Roger