Quotation marks indicate dialogue, someone else’s words, nonstandard words and phrases, exaggeration, and types of titles.
In American English, commas and periods always belong inside the final quotation mark. All other punctuation marks (exclamation points, colons, dashes, etc.) belong outside the final 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 (though this does not pertain to dialogue in fiction). Nonetheless, all major American style guides follow the American English standard, so all American writers should as well. (The only major exception I know is Wikipedia, which, through addled logic, practices the British standard, but no writer should treat Wikipedia as a source of good writing.)
Writers can opt for quotation marks rather than italics when indicating that a word should not be read in context of the sentence. While on this website I prefer italics for this purpose, as it requires fewer typographical marks, quotation marks are perfectly acceptable to denote a word as separate from the sentence: the word “octopus” is neither truly Greek nor Latin.
While quotation marks can overexpose a quality, don’t use them to indicate emphasis. The “intelligent” professor is likely not as knowledgable as he may like to think, and the “humble” musician talks far too much about her qualifications. Surrounding a word with quotation marks does not match the connotation of italicizing the same word.
Place the following titles in quotes:
•Short stories, chapters, articles, essays, most poems
•TV and radio episodes
•Songs, movements from larger works
When it comes to proper 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 belong to the years of typewriters. According to modern typographic practice, anyone who wishes to be typographically respected knows to use directional quotation marks (the same holds true for apostrophes).