Like the semicolon, there are a lot of misconceptions about when to use single quotation marks, and also like the semicolon, the rules are actually very simple. Mainly because there is only one.
Nonetheless, I see this punctuation mark misused all the time.
But before I get too far into this, it's important to note that I'm specifically talking about American English. British English reverses the use of double and single quotation marks--meaning British English uses single where American English uses double. Other than that, my understanding is, they are pretty similar (feel free to comment if you have more, relevant insight into British English).
In American English, the only time you use single quotation marks is when quoting something within a quote. For fiction, this usually means within dialogue, when a character is quoting something or someone else.
For example:
