Periods and commas go inside quotes without exception; colons and semicolons go outside quotes without exception.
Question marks go inside or outside quotes depending on where the question is being asked: If there is a question inside the quotes, the question mark goes inside; if there is no question inside the quotes but there is one outside, the question mark goes outside.
…He said, “What do you think you are doing?”
…Did he say, “What do you think you are doing?”
…Did he say, “I am not sharing this with you”?