Drop Other Punctuation
Before the closing parenthesis, drop almost all punctuation, such as commas, semicolons, and colons.
Retain a period inside the closing parenthesis if you've written a complete parenthetical sentence. Put the period outside the closing parenthesis if the parenthetical statement comes within the larger textual sentence.
His mind was clouded. (He hadn't thought of her in years.) But he shook it off and continued down the hill.
He enjoyed all kinds of fruit (especially apples, oranges, and bananas).