I watched a clip that was made a long time ago in the 1950s by Sid Davis Productions, Inc. The clip was published on YouTube, where I saw it.
You (probably) don't.
It is unlikely that a film made in the 1950s saw its first release on YouTube. You wouldn't cite an ebook as published on some torrent site, you wouldn't cite music as published on some file sharing site, and similarly you would not (usually) cite a film as being published on a video sharing site such as YouTube.
You would give YouTube as a source only if that film was actually first published on YouTube.
You do not give any details about the film you want to cite, so I cannot be more specific. Films are usually cited in MLA in the following format:
["Episode Title."] Movie or Series Title. Dir. Firstname Lastname. [Perf. Firstname Lastname, Firstname Lastname, ... .] Studio, [Day-as-Number Abbreviated-Month-Name.] Year. Medium of Publication.
The date is the first public viewing of a movie in a cinema or the first air date of a tv show or adverstising spot or the first publication date of a DVD and so on. It is not a re-release date, unless that version differs from the original and you want to cite that second edition specifically (as in the second edition of books).
Here are some examples from the Purdue Online Writing Lab, which gives more information on citing films of different kinds:
The Usual Suspects. Dir. Bryan Singer. Perf. Kevin Spacey, Gabriel Byrne, Chazz Palminteri, Stephen Baldwin, and Benecio del Toro. Polygram, 1995. Film.
"The Blessing Way." The X-Files. Fox. WXIA, Atlanta. 19 Jul. 1998. Television.
To find the relevant information for your citation, Wikipedia or IMDB may be of help.
It is not appropriate to append (possibly copyright infringing) internet "releases" of media (such as YouTube) to a citation.
If a movie is available, besides the official non-online release, online also, e.g. through an official or otherwise legitimate secondary release, such as an archive, museum or the director's website, then adding "Available online at http://..." is a nice gesture, but still not necessary. You don't append links to libraries that hold books you cite, either.
You would (and should) append the link to an online resource only if that was the channel of the first release (as e.g. in the case of Mischa Rozema's movie Sundays).