Quotation Marks with Other Punctuation

Commas and periods go inside quotation marks:

The name of the article is “Never Try This at Home,” and we all read it.

Semicolons and colons go outside if they are not part of the quoted material:

He told her he was “testing the waters”; indeed, he jumped off the bridge.

Question marks and exclamation points go either inside or outside, depending upon whether the quoted statement is part of the question or exclamation:

“I shall overcome!” he shouted.
Did he say, “I will balance the budget”?