U.S. English typological usage for dialogue in prose and journalism, known as typesetter's quotes, periods always go inside with one optional exception, unless not a part of cited or quoted text.

British English usage according to Hart's Rules or Oxford Guide to Style, periods always go outside and with single quote marks.

Online logical quotes according to Wikipedia online style manual, periods always go outside for cited text or quoted dialogue, unless the period is an internal part of the original text or quote. Always inside when quote marks are used to indicate emphasis. Emphasis is treated differently in other styles.

1 - In dialogue the period is always inside the quotes, unless the sentence ends in a tag, then there is not a period but a comma.

ex. Dad said, "Get in the car." (OR) "Get in the car," said Dad.

2 - In quoting a fragment of something said or the title of something that should be in quotes, it is preferable to put the period after the quotes.

...(the big red one).

...(the big red one.)

Inside when terminating a complete parenthetical sentence between the parentheses. Sentence capital case applies too.