To make the video start automatically when the page is opened you just have to add, just after the file path, "&autoplay=1". You can also make it loop at the end, by adding "&autoplay=1" after the file path.
For example:
<object width="425" height="350"><param name="movie" value="http://www.youtube.com/v/TZ860P4iTaM&autoplay=1"></param><param name="wmode" value="transparent"></param><embed src="http://www.youtube.com/v/TZ860P4iTaM&autoplay=1" type="application/x-shockwave-flash" wmode="transparent" width="425" height="350"></embed></object>
Note: videos can be inserted anywhere in the internal pages of the site, or in blocks created by you in the home page, not in the preset blocks of the home page.