APEX integrates the FullCalendar widget, but it doesn't duplicate its documentation. Have a look here for a list of the FullCalendar methods and options.
In general, most (interactive) APEX regions are implemented as jQuery UI widgets. That means you can use them like this:
$('selector').widgetName('methodName'); //invokes said method
$('selector').widgetName('methodName', 'param1'); //invokes said method with a parameter
$('selector').widgetName('option', 'optionName'); //gets a specific option
$('selector').widgetName('option', 'optionName', 'newVal'); //sets a specific option
What's more, you can inspect all available options by running:
$('selector').widgetName('option');
And even have a look at the internal object, see all methods, public and otherwise, via:
$('selector').widgetName('instance');
Moreover, via its region interface, APEX offers an even easier way to reach those methods and options, even without having to know a region's widgetName:
// this
$('widgetSelector', 'staticId').widgetName('methodName');
// is equivalent to
apex.region('staticId').widget().widgetName('methodName');
// is quivalent to
apex.region('staticId').call('methodName');
The last way is the shortest and doesn't require knowing the real widget's id or widget name.
All of this helps when dealing with regular APEX widgets, such as the Interactive Grid.
apex.region('emp').call('instance'); //inspects all methods
apex.region('emp').call('option'); //inspects all options
This however does not work on the FullCalendar region, for reasons that are beyond me. It should help you navigate all other APEX regions, but for the FullCalendar you'll have to resort to their API docs.
Hope this helps a bit.