If a question or exclamation is quoted directly, the quotation contains the question mark or exclamation point.
If the question or exclamation is at the end of the quotation, the question mark or exclamation point comes before the closing quotation mark.
Incorrect: "Look at that"! he exclaimed. "Did you see that"?
Correct: "Look at that!" he exclaimed. "Did you see that?"
(Question mark or exclamation point comes before quotation mark.)
A question mark can be found outside the quotation mark if the sentence is asking about a quotation, but the quotation itself is not a question.
Incorrect: Did Mark Antony say, "Friends, Romans, countrymen?"
(A question is not being quoted. The speaker is asking about a quotation.)
Correct: Did Mark Antony say, "Friends, Romans, countrymen"?
In the rare case where the question is about a quotation ending in a question, the sentence ends with a single question mark before the quotation mark.
Incorrect: Who said, "Et tu, Bruté?"?
(Second question mark redundant)
Correct: Who said, "Et tu, Bruté?"
See also Question Marks and Quotations with Other Punctuation Marks.