I always use double quotes, when writing, when quoting someone or to indicate something is "so-called".

Ann said: "That man is so attractive, I would love to marry him!" She was referring to Clark Kent, a.k.a. "Superman" or the "Man of steel".

To show exaggeration when writing (on paper) I use italics to indicate exaggeration. I also use them to emphasize points.
On-line I tend to *'s instead.

The only time I use a single quote is when I'm paraphrasing something.
John 3:16 says: "For God loved the world so much that he gave his only begotten Son, in order that everyone exercising faith in him might not be destroyed but have everlasting life."
As compared to:
What does that verse say again? Isn't something like: 'God loved us so much that he sent Jesus?' and that 'if we believe in him we'll be saved?'

I paraphrase the Bible a lot, so that's the only example I could think of right now lol.