The straight quotes " and ' on your keyboard are typewriter compromises. Typeset text uses curly quotes: “ ” for double and ‘ ’ for single. ’ U+2019 is also the recommended apostrophe (as in don’t). ″ and ′ are not quotes but prime marks, for feet and inches or minutes and seconds.
Languages differ. English uses “…” with ‘…’ inside. German uses „…“ and ‚…‘. French uses « … » with a narrow no-break space (U+202F) inside the marks. Swedish and Finnish use ”…” on both sides. Polish and Hungarian use „…”. Russian uses «…» with „…“ inside. Japanese and Chinese use corner brackets 「…」 with 『…』 inside.
Click any symbol to copy it. Names link to the full character page with every encoding.