About Mobile and Responsive Web Design in Google Sites
Google has produced a Mobile Friendly Test where Google will Analyze your site and determine if it is "mobile friendly" or not. This is somewhat subjective in the age now of Phablets (tablet sized phones) and ever increasing screen sizes (think iPhone 6 plus).
1. Design for Google Sites Automatic Mobile Adjustment (located in Settings > General > Adjust Site for Mobile)
Example: http://www.sitestemplate.net/business-templates (see Mobile Ready Material Design template)
2. Design for scaling to a smaller screen size.
Buy a Theme
We made a new Google Sites template based on Google's Material Design. It is available here for purchase: