To have a video start playing from a specific point, add "#t=" to a video's embed code, followed by the time at which you'd like the video to begin playing.
For example, if you want a video to start at 2 minutes and 30 seconds into the video, your embed code would look something like this:
<iframe allowfullscreen="" frameborder="0" height="315" src="http://www.youtube.com/embed/UkWd0azv3fQ#t=2m30s" width="420"></iframe>
