Take https://kouio.com for example (a Google Reader replacement I've built), in kouio you just enter a website's address and it'll discover the feed automagically.
<link rel="alternate" type="application/rss+xml"
title="Hacker News"
href="http://news.ycombinator.com/rss" />
Well as jerf mentioned below, HN doesn't correctly provide a link reference to its RSS feed. Now that's fine in our case, as a surprisingly large number of websites fail this test, and simply have a visible link with "rss" or "atom" in either the link's text or URL.
Now we pick these up, but in this case the front page of HN has an invalid link with "rss" in the text, namely this very thread itself. So normally the HN front page URL works fine, but right now it doesn't. This gives us a great chance to refine our discovery code a bit, so thank you!