When you add your Google account to an iPhone or CalDAV enabled device by default you will only see events from your calendar. If you someone has shared a calendar with you there is no clear way to make it available on your phone. Google has a tool to enable shared calendars to synch however to push you toward the Google apps Google has not made it easy for anyone else. Lucky for us the tool is simple to get to and use. Simply follow this link and check the calendars you would like to sync to your phone.

https://www.google.com/calendar/iphoneselect