Removing notification after click

Use the flag Notification.FLAG_AUTO_CANCEL

Notification notification = new Notification(icon, tickerText, when);
notification.setLatestEventInfo(context, contentTitle, contentText, pendingIntent);

// Cancel the notification after its selected
notification.flags |= Notification.FLAG_AUTO_CANCEL;

and to launch the app:

NotificationManager notificationManager = (NotificationManager) context.getSystemService(Context.NOTIFICATION_SERVICE);

// Create a new intent which will be fired if you click on the notification
Intent intent = new Intent(context, App.class);

// Attach the intent to a pending intent
PendingIntent pendingIntent = PendingIntent.getActivity(context, intent_id, intent, PendingIntent.FLAG_UPDATE_CURRENT);

To get the same effect using Notification.Builder or NotificationCompat.Builder call setAutoCancel(true) on the Builder instance.