Where do I find the standard licensing agreement on a video that's on YouTube?
From YouTube's help pages:

The standard YouTube licence remains the default setting for all uploads.

And Fair Use typically does not apply on the standard licence. See here for specifics, and when it does apply. The other option is Creative Commons:

Creative Commons licences provide a standard way for content creators to grant someone else permission to use their work. YouTube allows users to mark their videos with a Creative Commons CC BY licence.

Videos licenced under CC by Attribution 3.0 have this in the info under the video (you may need to click on Show More)

Licensed under Creative Commons: By Attribution 3.0 License
http://creativecommons.org/licenses/by/3.