How do I delete my website from the Google index ?

There are instructions on one of the Google pages.

If you want to delete your entry from Google's index AND take the site down, then you need to remove the content (so it returns 404 errors) and then choose Google's remove from index option (you specify your now-defunct URL). I guess you have to remove your content first so as to prevent malicious index-removals.
If you want your site to remain present for those-in-the-know, but just not indexed in search engines, then use the robots.txt file as other posters suggested. Google offers info on the format of robots.txt - tis very straightforward.