How to incorporate AMP in an existing theme?
The AMP project for Drupal has three parts. The AMP module, the AMP PHP Library, and the AMP Theme work together to provide valid AMP markup for nodes with AMP-enabled content types at paths with ?amp at the end of the URL.

From the AMP module page: 


  The AMP module is designed to convert Drupal pages into pages that comply with the AMP standard. When the AMP module is installed, AMP can be enabled for any node type. At that point, AMP content becomes available on URLs such as node/1?amp or node/article-title?amp. 
  
  The AMP PHP Library analyzes HTML entered by users into rich text fields and reports issues that might make the HTML non-compliant with the AMP standard. The library does its best to make corrections to the HTML, where possible, to make it more compliant with the AMP HTML standard.


From the AMP Theme page: 


  The AMP Theme is designed to produce the very specific markup that the AMP HTML standard requires. The AMP theme is triggered for any node delivered on an ?amp path.


Some additional reading, an article describing the three in more detail on the official AMP blog: AMPing up Drupal.