You cannot. While there are ways to pull YouTube videos for playback on Roku, it is disallowed by the
YouTube Terms of Service. If you want to stream videos, you'll need to host them on your own CDN.
"YouTube TOS, Section 4.C." wrote:
You agree not to access Content through any technology or means other than the video playback pages of the Service itself, the Embeddable Player, or other explicitly authorized means YouTube may designate.
My Channels: http://roku.permanence.com - Twitter: @TheEndlessDev
Instant Watch Browser (NetflixIWB), Aquarium Screensaver (AQUARIUM), Clever Clocks Screensaver (CLEVERCLOCKS), iTunes Podcasts (ITPC), My Channels (MYCHANNELS)
