At Admin Panel -> Settings -> Switches, you have a "Calendar" option. When you switch on the calendar, a calendar menu item appears in the top bar of the site's front end. Click that to go to the calendar page, which displays a calendar with upcoming events written on it (and since version 9.0 also has a toplist of the next upcoming events). Members (not guests) have the option of subscribing to the calendar for notification of new events by clicking the subcription link below the calendar.

To determine who can submit and edit events, go to Admin Panel -> Members -> Manage Usergroups.

There's a separate option to decide whether to include member birthdays on the calendar. If you enable this, the birthdays of active members will be displayed on their appropriate dates on the calendar. At Admin Panel -> Settings -> General you can set how recently the member needs to have logged in for their birthday to be listed. If you have a very large number of members (10,000+) you may notice a slowdown in viewing the calendar, and can speed things up by setting it to show fewer birthdays.

There's another separate option for article calendards, which creates a calendar for each article on the article details page where the article owner can fill in a quantity for each day (this is used by sites where something is being reserved that has a limited quantity available per day). For more about that, see the quantity reservation calendars article.