Here are the rules for punctuation with closing quotation marks.

Semicolons and colons always go outside the closing quotation marks.  Examples:
> Here are some main ideas in the essay entitled “Of Studies”:
> On one side of the auditorium, people were singing “Hail to the Chief”; on the other side, they were chanting protests.

A question mark goes inside the closing quotation marks if the quoted material is a question: 
He asked, “When do we eat?”  “What is serendipity?” he asked.

The question mark goes outside if it belongs to the sentence and not to the quoted material:  Did the parrot say, “Give Polly a cracker”?  Did you call me a “moron”?  Do you know the meaning of “serendipity”?  Exclamation points follow the same principle.

In the United States, periods and commas always go inside the closing quotation marks.
> The essay was originally called “An Agnostic’s Faith,” but the author renamed it “An Agnostic’s Belief.”
> If he keeps calling you “Sam,” don’t be upset; he calls everyone “Sam.”
> In an article headlined “The Politics of Trash Talk,” George Will asserts that both presidential candidates are speaking “with studied irrelevance.”

However, the rest of the world treats commas and periods differently than the U.S. does, placing commas and periods inside or outside the closing quotation marks depending on the whether the period or comma belongs to the quoted material or to a larger part of the sentence.  They are, in essence, applying the same logic to the comma and period that is applied to the exclamation point and question mark.

Here’s a quote from the British journal, The Economist:
. . . tax cuts for the better-off would be matched by an increase in the “job bonus”, a sort of tax credit for those too poor to pay an income tax.  (The comma goes outside because it separates the appositive phrase from the rest of the sentence.)  In the U.S., the comma after “tax bonus” would go inside the closing quotation mark:  . . . an increase in the “job bonus,” a sort of tax credit for those too poor to pay an income tax.  (This is because it is conventional in the U.S. to put commas and periods inside the closing quotes – no matter what.)

Whether the globalization of communications will bring English-speaking countries into accord with regard to use of the comma and period with closing quotation marks remains to be seen.  So far, this outcome does not seem likely.  Newsweek still writes:  Mario began his career in “Sweetback,” playing his father’s character as a boy.  The Economist, however, would write:  Mario began his career in “Sweetback”, playing his father’s character as a boy.