You can start watching a YouTube video from a specific time by adding "#t=XmYs" to the URL, where X is the minute and Y is the second from where you want the video to start.
For example, if you want to start playing the following video from the 5th second
Code:
http://www.youtube.com/watch?v=UkqIZvsjn2I
just add "#t=0m5s" to the URL:
Code:
http://www.youtube.com/watch?v=UkqIZvsjn2I#t=0m5s
Alternatively you can use
YouTubeTime, a web-site that allows you to enter a YouTube URL, minutes and second to start playing from a specific time.