You can embed a YouTube video using the video ID (the series of numbers/letters that are at the end of the page link following v= ). Adding [[Category:Video]] at least once on any page with a video will allow easier searching.
Other video sites are supported as well as other options (sizing, alignment), for details see How To Embed a YouTube Video/Details.
Code Edit
<youtube>VideoID</youtube> [[Category:Video]]
Example Edit
For example:
<youtube>uiC_XPpnn4k</youtube>
displays as:
<youtube>uiC_XPpnn4k</youtube>