Google announced last month that Google Video will become a search engine that will include videos from different video sites. For the moment, Google Video includes YouTube videos in the search results.
Because YouTube is much more popular than Google Video, much more videos are uploaded to YouTube (Google Video has 3 million videos, while YouTube has 18 million videos), so most search results will contain a lot of YouTube videos. If you want to search only YouTube videos, you can do that at youtube.com, but how to restrict your search only to Google videos?
Use the site: operator, that should be familiar from web search or image search. Append this to a query: site:video.google.com. For example, to search for Regina Spektor, use this query: [regina spektor site:video.google.com]. To restrict the search to YouTube files, add site:youtube.com to the query.
An interesting tidbit is that the search results feed contains only results from Google Video (you can obtain the feed by adding "&output=rss" to the URL or by clicking on the RSS links from the top of the page).