Visit Settings > Integrations to connect your Google Calendar. Clicking "Sign in with Google" will open up Google's OAuth screen in a new window.

Connect to Google calendar to create, manage, & update shared calendars for your community. All events will be synced to your Google calendar instance and Heartbeat will automatically send calendar invites to members for new events.

You will only be able to create, edit, and push calendar events if you are a community administrator with the appropriate permissions.