The bad news: The webcam currently doesn't have live access to the internet.
Here's the official update:
Quote
California Nevada Applications Program/California Climate Change Center
28 October 2011
Tioga Pass webcam status
The Dave Peterson Memorial Tioga Pass Camera is in place and taking photos. However, we are waiting for permission from the park service to access their internet. The phone line internet access at Tioga Pass was removed when the park switched to a satellite internet provider. At this time we do not have permission to access thier internet link and we are unable to relay images.
http://tenaya.ucsd.edu/tioga/