You can retrieve the content of any public Google Spreadsheet in your web app using JSON feeds. The sharing permissions of the Google Spreadsheet should be either “Public” or set to “Anyone with link can view” for the app to fetch cells from the Google Spreadsheet without authentication.
You will also need to publish the sheet (File -> Publish to the web -> Publish) for the data to be accessible from your website or REST powered web app.
The JSON and XML feeds for any Google Spreadsheet is available at:
Here’s a sample jQuery based example that pulls data from a public spreadsheet in Google Drive as JSON and prints as HTML. This can be clubbed with IFTTT or Zapier for more useful integrations.