This is a read-only calendar. You can only add events on the remote calendar.
Google Calendars use the iCal standard format. This guide will walk you through how to use a Google calendar in the Calendar module using the iCal format.
For more information about the Calendar iCal see Calendar iCal
Add a Google Calendar
Login to your Google Calendar account
From the calendar list on the left click the expand arrow to bring up more settings. Click "Calendar Settings"
In the Calendar Details screen look for "Private Address". Notice that it has an ICAL logo.
Click the ICAL button.
Copy the ical link (don't click it as that will just download the file). Now go to the calendar module. Click "Add Remote iCal Calendar"
Name: The name of the calendar
Description: The description of the calendar
Remote URL: The ical link you copied from above
Synchronization Time: How often to sync the remote Google calendar with the local calendar
Click save and your google events will now show up in your local calendar and will update based on your synchronization time settings.