I know that they are used inside double quotes for a quotation within a quotation, but when else should they be used? I've seen them used in all sorts of syntactical situations, but where do I find a comprehensive guide to its proper usage?
A quick search turned up this similar question on another site.
In short, quotes within quotes are the main usage of enclosing single quotes. Another common usage is for quotes in a title or headline. Of course, the same character is used for apostrophes when typing, as the QWERTY keyboard has never had separate keys for an apostrophe and a single quote (the look of which CAN differ subtly depending on the typeface).
According to this other page, in British English, single-quotes and double-quotes have historically been reversed in terms of preference; normally, quotations should be enclosed in single quotes, and double-quotes are used for internal quotations. This preference is still present but fading in the UK, and American usage has always preferred double-quotes for the initial quotation and single for internal quotes.
Unofficially, I have sometimes seen single quotes used to denote thought instead of speech. More commonly, the thought is italicized, or no formatting is applied at all; these styles are more correct, and if you had written a manuscript employing single quotes in this manner, they'd likely be removed or replaced by your editor or typesetter.
Single quotes are used in formal works of philosophy and linguistics to mark off words being discussed as words, or used in a special sense. For example:
This implies that ‘Hesperus’ and ‘Phosphorus’ are different names for the very same planet, which in turn implies that the sentence ‘Hesperus is the same planet as Phosphorus’ is true.
Single quotes are easier on the eyes when reading material that uses quotes frequently, which is why academic publishers adopted this format for works in these areas.
In Computer Science double quotes represent a String and single quotes represent a Character.