The Calendar API is available as of Android 4.0.
Creating new events is done via Intents and does not require any permission. Setting properties of the event is done via Intent extras. The user will be prompted if the event should be created.
For example the following will prompt the user if an event should be created with certain details.
Intent intent = new Intent(Intent.ACTION_INSERT);
intent.setData(CalendarContract.Events.CONTENT_URI);
startActivity(intent);
You can also add dates and time, if this event is repeated and the like. See the comments in the coding for examples.
Intent intent = new Intent(Intent.ACTION_INSERT);
intent.setType("vnd.android.cursor.item/event");
intent.putExtra(Events.TITLE, "Learn Android");
intent.putExtra(Events.EVENT_LOCATION, "Home suit home");
intent.putExtra(Events.DESCRIPTION, "Download Examples");
// Setting dates
GregorianCalendar calDate = new GregorianCalendar(2012, 10, 02);
intent.putExtra(CalendarContract.EXTRA_EVENT_BEGIN_TIME, calDate.getTimeInMillis());
intent.putExtra(CalendarContract.EXTRA_EVENT_END_TIME, calDate.getTimeInMillis());
// Make it a full day event
intent.putExtra(CalendarContract.EXTRA_EVENT_ALL_DAY, true);
// Make it a recurring Event
intent.putExtra(Events.RRULE, "FREQ=WEEKLY;COUNT=11;WKST=SU;BYDAY=TU,TH");
// Making it private and shown as busy
intent.putExtra(Events.ACCESS_LEVEL, Events.ACCESS_PRIVATE);
intent.putExtra(Events.AVAILABILITY, Events.AVAILABILITY_BUSY);
More about this article
and more calendar api tutorials
Mobile tut plus tutorials
Official Calender Documentation
Here is another good simple calender example tutorials.