Quotation marks indicate dialogue, someone else’s writing, nonstandard words and phrases, exaggeration, and certain titles.
American English always places commas and periods inside the closing quotation mark. All other punctuation marks (exclamation points, colons, dashes, etc.) belong outside the closing quote unless those marks belong to the quoted text. “You are right,” she said. Is he a “changed man”? This list contains all his known “aka’s”: Bob, Fred, and “The Hombre.” To the confusion of many writers, British English only punctuates inside the closing quote when the punctuation mark belongs to the quoted material (this does not pertain to fictional dialogue). The only major exception I know to the above American–British divide is Wikipedia, which, through addled logic, allows whichever style the writer prefers, much to the detriment of consistency.
Writers may use quotation marks in place of italics to indicate that a word should not be read in context of the sentence. But do not to use quotation marks for emphasis—they will act as sarcasm. The word “octopus” is neither truly Greek nor Latin works as intended, but The “intelligent” professor suggests a professor of mocked intelligence.
Parts of larger works are usually placed in quotation marks. The following list gives a general idea of what normally falls within quotes, but refer to your style guide for proper formatting:
•Short stories, chapters, articles, essays, most poems
•TV and radio episodes
•Songs, movements from larger works
When it comes to formatting, always prefer the directional, curly, or “smart” quotation marks. These are the curved quotations your computer and word-processor automatically curl to the correct left or right direction. Straight quotation marks, as shown "here," belong to the years of typewriters. According to modern typographic practice, anyone who wishes to be typographically respected should use directional quotation marks (the same holds for apostrophes).