When I drop a YouTube link in my page, it embeds the video at 150×150. I have tried to use a shortcode to change the size and the shortcode doesn’t resolve to the video, it stays as text.
Try [embed width="480" height="360"]URL[/embed]. The [youtube] shortcode is available on WordPress.com and in Jetpack, but it’s not part of the core WP software.
If you take a look at the codex here – http://codex.wordpress.org/Embeds
you’ll see that all you need to do to post embed youtube videos is to just paste the link.
If you go to your settings area under media, you can change the size of the videos.