What is the most reliable way to check the accuracy of a website?

Well, journalists check accuracy by finding a second (or third) source that says the same thing.

But it's also useful to find out who the author is, who they work for, whether the other things they've said make sense.

Anybody can say anything in the comments section or on their own blog.  But there are actual editors who check the accuracy of statements made on mainstream news sites like the New York Times, or the major television networks.  In the U.S. I find National Public Radio a reliable source.