Installing and loading google client php api
Here's an updated answer (the version of the client library I'm using is  "google/apiclient": "1.0.*@beta")

    function hook_libraries_info() {
     $libraries['google-api-php-client'] = array(
     'name' =&gt; 'Google API PHP Client',
     'vendor url' =&gt; 'http://developers.google.com/api-client-library/php',
     'download url' =&gt; 'http://developers.google.com/api-client-library/php',
     'path' =&gt; 'src/Google/',
     'version' =&gt; '1',
     'files' =&gt; array(
      'php' =&gt; array(
        'autoload.php'
      )
    )
  );
  return $libraries;
}


Note, the 'autoload.php' file in the files array.  This will automagically load all the classes you might want, and seems to work well for me; rather than manually selecting each file the library includes that I might need.

I load the library and then use it like this:

$library = libraries_load('google-api-php-client');
module_load_include('inc', 'page_speed', 'page_speed_client');


My inc file contains the logic I want for defining a new client and service (see the Google docs) and does a Pagespeed Insight query, and (for now) simply dumps the returned data onto a page.

Final caveat, remember to clear cache if you edit your files array, otherwise the library won't load properly, that caught me out a couple of times.