To use google calendars you need to have a google account and add it to your Android phone.

To sync your Google Calendar data between Google cloud and the Android calendar storage, you need the Google Calendar app installed. (Early versions of Android included a Google Calendar sync adapter, but this was moved to the Google Calendar app, to be able to update via Google Play. Alternatively you can configure Google as CalDAV calendar, but this has several limitations.)

The Google Calendar sync to Android has some limitations:

Please see also: Problems with Google Calendar Synchronization