Start the video at the YouTube page and right click on anywhere on the video screen. Now select “Copy Video URL at current time”.
This will copy the URL of the video starting from that current time to the clipboard. That’s all. You can now paste that link to share with your friends. Whenever the link will be clicked, the video will start from that time while you grabbed the URL.
Youtube now allows you to link to a specific time of its videos using the t hash parameter.
For example, if you want the video to start at the 1min, 20sec mark then add #t=1m20s to the URL.