Knowing how to punctuate properly can be confusing when we are dealing with quotation marks.
I use the Chicago Manual of Style and this is what they recommend:
Periods: put the period inside the quotation marks.
For example, Jim said that his mother was "out of breath."
Question Marks: this depends on whether the words in quotation form a question or not.
For example, Jim asked his mother, "Are you going out to play bridge?" Are you going out to play bridge is a question, so we want the question mark inside the quotations. But what if I rephrase the example as such? Is Jim's mother a real "whiz" at bridge? In this instance, the whole sentence is a question, so we put the question mark at the end of the sentence, not within the quotations.
Colons and Semicolons: these go outside the quotation marks.
For example, Jim told Andy that he "loved living in Florida"; summer was his favorite season. Or, Jim told Andy that he used to love "living in Ontario": too cold for him now though. Notice that the main difference between my using the semicolon and the colon was that the former separated two independent clauses that could stand alone, and the latter was followed by a dependent clause that could not stand alone.
Happy writing!
Sigrid