You will be notified by email when someone shares a calendar with you. The permission settings that they assign to you will determine if and how you can add the calendar to your list of calendars in the left sidebar of Google Calendar.
Make changes AND manage sharing: The calendar will automatically be added to your list of My calendars in the left sidebar of Google Calendar.
Make changes to events: The calendar will automatically be added your list of Other Calendars in the left sidebar of Google Calendar.
See all event details: You will receive an email notice that the calendar has been shared to you and it will contain a link to add the calendar to your list of Other Calendars. See example below.
See only free/busy (hide details): You will receive an email notice that the calendar has been shared to you, but you will not receive a link to add the calendar to your list of calendars.
Email Notice that a Calendar Has Been Shared to You
Contains the "add the calendar" link depending on your permission settings.
