Hey this is what i'm implementing in my app for you tube video play
    public class Youtubevideo  extends YouTubeBaseActivity implements YouTubePlayer.OnInitializedListener
{
    public static final String API_KEY = "Use Your API key For youtube api";
    //http://youtu.be/<VIDEO_ID>
      //sample video id
    public  String VIDEO_ID = "abcdefgh";
    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        /** attaching layout xml **/
        setContentView(R.layout.youtubevideo);
       Intent dataReceived = getIntent();
        if(dataReceived != null)
        {
           VIDEO_ID = dataReceived.getStringExtra("url");
        }
        /** Initializing YouTube player view **/
        YouTubePlayerView youTubePlayerView = (YouTubePlayerView) findViewById(R.id.youtube_player);
        youTubePlayerView.initialize(API_KEY, this);
    }
    @Override
    public void onInitializationFailure(Provider provider, YouTubeInitializationResult result) {
        Toast.makeText(this, "Failured to Initialize!", Toast.LENGTH_LONG).show();
    }
    @Override
    public void onInitializationSuccess(Provider provider, YouTubePlayer player, boolean wasRestored) {
        /** add listeners to YouTubePlayer instance **/
        //player.setPlayerStateChangeListener(playerStateChangeListener);
        //player.setPlaybackEventListener(playbackEventListener);
        player.setFullscreen(true);
        player.setShowFullscreenButton(true);
        /** Start buffering **/
        if (!wasRestored) {
            player.cueVideo(VIDEO_ID);
        }
    }
    private PlaybackEventListener playbackEventListener = new PlaybackEventListener() {
        @Override
        public void onBuffering(boolean arg0) {
        }
        @Override
        public void onPaused() {
        }
        @Override
        public void onPlaying() {
        }
        @Override
        public void onSeekTo(int arg0) {
        }
        @Override
        public void onStopped() {
        }
    };
    private PlayerStateChangeListener playerStateChangeListener = new PlayerStateChangeListener() {
        @Override
        public void onAdStarted() {
        }
        @Override
        public void onError(ErrorReason arg0) {
        }
        @Override
        public void onLoaded(String arg0) {
        }
        @Override
        public void onLoading() {
        }
        @Override
        public void onVideoEnded() {
        }
        @Override
        public void onVideoStarted() {
        }
    };
}
and xml will be like:
<LinearLayout xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:tools="http://schemas.android.com/tools"
    android:layout_width="match_parent"
    android:layout_height="match_parent"
    android:orientation="vertical" >
    <com.google.android.youtube.player.YouTubePlayerView
        android:id="@+id/youtube_player"
        android:layout_width="match_parent"
        android:layout_height="wrap_content"
        android:background="#fff"
        android:padding="5dp" />
</LinearLayout>
and in build.gradle use the Youtube jar lib openly available:
compile files('libs/YouTubeAndroidPlayerApi.jar')
hope this will help.
:)