The Events Slug URL
The URL of your calendar depends on the Events Slug URL setting found in the Events > Settings > General screen. By default it's set to events, so your calendar URL would be example.com/events.
If you're not sure where your site's calendar is located, you can easily determine this by visiting the aforementioned admin screen and viewing the options shown in the following screenshot:
☝️ As you can see, a preview of the actual URL on the site is provided.
The Single Event URL Slug
While the Events Slug URL is used for the various calendar views, the Single Event URL Slug is used for individual events. The default Single Event URL Slug is /event. So, for example, an event called "Christmas Party" would exist at example.com/event/christmas-party.
Both URL slug options—the Single Event URL Slug and the Events Slug URL—can be changed on the aforementioned Events > Settings > General wp-admin screen.
How Do You Make the Calendar the Site's Home Page?
With our release of 4.4, you can now set your calendar as the homepage! Visit Events > Settings > Reading and make sure the "Front page displays" setting is set to A static page and select Main Events Page for the "Front page" setting.
You can learn more ways to make your calendar the site's homepage here.