Admittedly I haven't played with the Xbox YouTube app much. I looked through various tabs and menus and could not find a way to perform a keyword search. Is there a way?
In the current incarnation (March 2012), hit Y to be presented with the search interface (it's displayed at the bottom left-hand corner of the screen). You can use the controller to enter a search query, or use gestures to select characters with Kinect. It does not currently have support for voice control through the Kinect.