In the next screen you have the option to sync Mail, Contacts, and Calendars. To sync only calendars, flick the switch next to the Calendars entry to On and flick the Mail switch off. To keep your existing events on your iPhone, tap the Keep on My iPhone button that appears. Verify that you want to do this when the Keep on My iPhone button reappears. Tap Done at the top of the Exchange screen.

To choose the calendars to sync, launch Safari on the iOS device and travel to http://m.google.com/sync. Enter your Gmail username and password when prompted. Tap the name of your iOS device in the Manage Devices screen that appears. In the resulting Settings screen, tap on the shared calendars that you want to sync with your iPhone, iPod touch, or iPad.

Now, when you launch the Calendar app, tap the Calendars entry at the top of the screen. In the Calendars screen that appears you’ll see an entry for your Gmail Exchange account that lists all the shared calendars you’ve chosen. When someone in your family updates their Google calendar, those events will sync to your iPhone.