Open your Settings app, then tap ‘Mail, Contacts, Calendars.’
This section is where you’ll be able to add your calendar to iOS. You’ll need to tap on Add Account, then select Google from the list of default providers. From here, sign into your Google Account; the next screen will show a list of permissions to access your Google Account: view and manage emails, view and manage calendars, etc. Tap Allow.
The final screen has a series of account toggles that determine what data gets synced between your iPhone and Google’s servers. These are handy if you don’t wish to receive email on your mobile device, but don’t want to sync your calendar (or vice versa).
If you see a Gmail account already listed, you might have added it when you first turned on and activated your iPhone. To make sure your Google Calendar is added, tap the Gmail account in question. It will bring up the previously mentioned screen with toggles for Mail, Contacts, Calendars, and Notes. Make sure the toggle beside ‘Calendars’ is green.
If you have more than one Google Calendar, you can choose which to sync.
Google provides an older tool for iPhone users trying to figure out which Calendar is synced to their iPhone; you can access it here. Of note is that you aren’t limited to a single Calendar, so if you wish to set up multiple calendars and pick and choose which go to the iPhone, you can.
If you make it through the steps to add your calendar only to find you don’t like the built-in iOS Calendar app, there is hope. In addition to critically acclaimed solutions such as Fantastical, available from the App Store, Google has released their own Calendar only app.