The best way I’ve seen it done is by using the Slider plugin that comes with the Ally theme – http://demo.appfinite.net/ally
You can purchase the plugin separately by going here directly – http://codecanyon.net/item/layerslider-responsive-wordpress-slider-plugin-/1362246
Here is a Full Width example – http://kreaturamedia.com/layerslider-wordpress-full-width-slider/ …and as you can see this plugin allows you to add videos. So if you were to use this plugin or any plugin like it, all you would have to do is set it up and add it to your Full Width (Slider Wide) widget area and it should show up fine.
Thats about the easiest way. Anything beyond an already built plugin will require some custom code……Much cheaper to just purchase the plugin since it already works 馃槈