I had a friend ask me to explain this once and for all. Where does the blasted period go? Quite simply, put the period on the outside if it isn’t a complete sentence. Put it on the inside if the complete sentence is surrounded by the parentheses.

For example:

Outside - Johnny went down to play ball and forgot his mitt (it was in the garage).

Inside - Johnny like playing ball. (He like catching the most.)

Do note a single (  is a parenthesis. A pair is parentheses.