To configure your Nest calendar with an iPhone or iPad, log into your Nest account on a web browser.
Click the Settings button in the bottom left hand corner of window. Copy the WebDAV link that appears.
https://nest.greenant.net/remote.php/dav/principals/users/<YOUR USER NAME>/
In your iOS device, go into the Settings application. Open Mail, Calendars, Contacts and select Add Account.
A list of service providers will appear. Selet the Other option at the bottom then select Add Account.