I use this widget to display my shift calendar - see the screenshot below
This widget works with API v3 and requires a service account to be set up via the Google Developer's Console. Once a project is set up, enable the Calendar API. On the Credentials page create a new OpenID and download the p12 key file - set up the path to this file in the job file and grant the email address access to the relevant calendar.
The job file defines how many events to get from the calendar and when to start the search. My version gets the next 6 events.
Add to Gemfile:
gem 'google-api-client', '>= 0.8'
#= require moment.js to the application.coffee script. You can also use
moment.min.js if you've downloaded that.