" v.s. ', which one do I use

I don't say a lot of really good, memorable, or awe-inspiring things. I like to quote people who do though. I always seem to run into the problem of not knowing which one to use between the two formats and for a long time I thought it was personal preference until I got to college and I started getting marked for "incorrectly citing". No one ever told me how to use them, so I looked it up for this post.
The Purdue University Online Writing Lab says that
Use single quotation marks for a quotation enclosed in another quotation. And the example they give is: The agricultural reporter for the newspaper explained, "When I talked to the Allens last week, they said, 'We refuse to use that pesticide.' "
http://owl.english.purdue.edu/handouts/grammar/g_quote.html