Google Play Services

I made an example that shows how can access to the YouTube API v3 from an Android app that works very well:

http://lookthiscode.blogspot.com.ar/2013/01/utilizando-youtube-data-api-v3-desde.html

Actually this example is based in the official example that shows how to use the task API from an Android app. I modified the example to use the YouTube API authentication scope.

The article is in spanish but you can download the source code of the project using the link at the end of the article.

The main piece of code to solve your problem is the following:

// Google Accounts
credential = GoogleAccountCredential.usingOAuth2(this, YouTubeScopes.YOUTUBE, YouTubeScopes.YOUTUBE_READONLY);
SharedPreferences settings = getPreferences(Context.MODE_PRIVATE);
credential.setSelectedAccountName(settings.getString(PREF_ACCOUNT_NAME, null));
// YouTube client
service =
        new com.google.api.services.youtube.YouTube.Builder(transport, jsonFactory, credential)
            .setApplicationName("Google-YouTubeAndroidSample/1.0").build();