Most of the time you can copy the site's URL into Google Reader and it will try to find the proper RSS feed. It works for blogs hosted on Blogger and Wordpress, at least; not sure how it does it.
The same way that some browsers do it. There is a meta-tag in the page, which describes which feed formats are available, and where to find them.
For one thing, it shows you the whole history of the feed -- even when the XML itself contains just the few most recent items.