I don't think you can post short "videos" on here unless they are in the animated .gif format. If you have a video in this form, you can just show it off the same way you would a picture with the [img] tags. They will play spontaneously since your browser has a plugin to handle those videos.
If the video is in some other form, like an .mpeg or .avi or .swf, you'll have to just link to it as a URL and let people click on it from there. I don't think there is a way for the board to spontaneously start these type of videos because it requires another peripheral (Media Player, etc.) to start up.