1. Writing Wisdom
Use of quotation marks

2. Exact language
The primary function of quotation marks is to set off and represent exact language (either spoken or written) that has come from somebody else.* 
Mr. Cook, who was wearing his favorite Hawaiian shirt, said, "The students of Cleveland amaze me with their creativity.”
Mr. Cook, who was speaking about Cleveland students, said they, “amaze me with their creativity.”
*From the Purdue Online Writing Lab

3. To Indicate a specific title
Song
Poem
Short story
Essay
Episode of a radio/tv show
Chapter of book
Article in a magazine, newspaper, web
NOT book titles, magazine titles, television show titles, etc., which are underlined or italicized.

4. Unnecessary or “erroneous” use
The use of quotation marks to denote irony or emphasis is becoming more common in casual writing.
He works so hard at sounding “correct,” but his deep southern dialect gets in his way.
NOT to be used with formal, academic writing.
When writing about texts, the use of quotation marks will tell the reader you are quoting from the source material.

5. Exception to the Rule
In the study of language (a.k.a. linguistics), it is correct to use quotation marks to indicate a particular word or phrase under scrutiny.
While considering the essays on language, the use of the words “correct” and “right” take on a new meaning.