Head over to the video you want to share and
Click on " share" button under the YouTube video
Select the check box for "start at" then enter a time value in the text box next to it. A link will be generated for you in the left of the check box .
The second tip Chris provided is my favourite. You only have to add the string
#t=xmysto the end of any YouTube URL. x represents the number of minutes and y represents the number of seconds. For instance the URL of the video you want to share is ( http://www.youtube.com/watchv=J6ZzmqDMhi0) and you want to share only the part that starts at 3 minutes and 2 seconds meaning you need to add the following string (#t=3m2s) to the original URL. The entire URL will look like this http://www.youtube.com/watch?v=J6ZzmqDMhi0#t=3m2s.