Parentheses may surround words, phrases, and sentences (though should not surround multiple consecutive paragraphs). When a sentence falls within parentheses, the final punctuation belongs inside the closing parenthesis. When parentheses fall within a sentence, the final punctuation belongs outside the closing parenthesis—as shown in the first sentence. If parentheses within a larger sentence contain a whole sentence, only punctuate before the closing parenthesis if using a question mark or exclamation point: I left yesterday (did I turn off the stove?) and shall return tomorrow (it’s been a short, but tiring, trip).
Parentheses serve numerous specific functions, of which the most common are interjections, notes, asides, and explanations: His name was Jonathan (but wanted everyone to call him Jon). Parentheses for these situations may be optional—rephrasing or rewriting with em dashes or commas may suffice if the writer wishes to avoid using parentheses. Citations, per certain style guides, may require parenthetical references within the text (see below paragraph for an example). Parentheses can also clarify text through definitions and übersetzungen (translations).
Bryan A. Garner warns against overusing parentheses, as “they tire the reader’s eye . . . and deaden the reader’s interest” (Garner 752). I have not read this advice elsewhere, though I tend to agree for another reason: Parentheses’ vertical nature impedes the horizontal flow of the eye far more than does the sleek em dash. And many a lazy reader, even if well-intentioned, sees parentheses as optional and may skip them entirely.