At the moment (up to version 2.4.x) there is no standard widget for showing (youtube) video's.
You can show a static video on your start page (see this question). But that question only deals with video's on your start page! Video's on a start page is possible by adding a youtube HTML tag in your theme package (startpage.mxf). But editing other .mxf files is absolute no option, they will be overwritten when deploying your project.
In short: you need a custom widget for showing the video's.
Note: Uploading and downloading video's is no problem, use the file manager widget for that.