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The Calendar module is one of those modules that seems like it should be dead-simple to use, but often overwhelms site admins once they get their first look at it (actually, it is pretty easy to use).
The Calendar module is basically just a great big Views add-on. It requires the Date module as well, but all of its user interface is done via Views.
Assuming you already have a content type set up for events (this is a "Quick" tip, after all), you really only need to change three things in the default display of the "calendar" view.
That's basically it! You don't need to touch any of the other displays, just save the view and then go to /calendar and check out your big bad self! Still confused? The Calendar module page has some links to some great tutorials.