This feature has now been around for a little while, but it's not that well known. Also it can be hard to find information about it online as people often call it deep linking - which makes sense if you know the jargon but isn't the sort of phrase you'd otherwise guess is the one to look for.
So here's how to create a link to a YouTube film which will start it playing part way through:
http://www.youtube.com/watch?v=o4L0pWUNp08#t=0m39s
The key parts are:
o4L0pWUNp08 - which is the unique reference code for the video. If you are watching a film on its own page on YouTube, you'll find this in the URL (address bar). If you are, say, viewing the film on a channel page, click on the "View comments, related videos and more" link underneath the video and this will bring up the clip's own YouTube page.
0m39s - which is the starting time; in this case it means start playing 0 minutes and 39 seconds in to the film.