More so now than ever before, quality information comes in many different formats. Just like blogging opened up the written word to millions of new people, the simultaneous development of streaming media and cell phone cameras has reduced the barrier of entry to people interested in making and sharing video content. Some of this content is incredibly valuable, well-researched, and interesting, and can be used to support your arguments.
You cite your sources both to give credit to the scholars upon whose work you are building and to place your own research within that lineage. Just like you need to cite books and articles that you use in papers, you need to cite video too. There are a lot of different kinds of video, so here, I'll provide three different examples for MLA and APA. But the same general rules apply regardless of whether you're pulling from a PBS documentary, a feature film from the 1920's, or a Vine.