There was a post this morning asking about how many people disable JavaScript. Then I began to wonder what techniques might be used to determine if the user has it disabled.
People have already posted examples that are good options for detection, but based on your requirement of "give warning that the site is not able to function properly without the browser having JS enabled". You basically add an element that appears somehow on the page, for example the 'pop-ups' on Stack Overflow when you earn a badge, with an appropriate message, then remove this with some Javascript that runs as soon as the page is loaded (and I mean the DOM, not the whole page).