If you're writing direct speech, the quotes normally come outside the terminal point (full stop, question mark, etc.) or comma:
The conductor asked me, "Have you got a bus pass?"
"I'll collect the tickets next week," said Emma.
Ed said, "I'll see what I can do."
Kim shouted, "Get off me!"
"If I'm going to lend you money," said Alex, "at least let me know what it's for."
But if you're using quotes to emphasise something or show it as an example (as we do on this website), then the quotes should be inside the terminal point:
A good example of a noun phrase is: "The big black car".
An example of the superlative is: "Kim is the oldest of them all".
You can use single quotes ('..') instead of doubles ("..") if you prefer.
There may be variations of this in the US. Perhaps a native speaker of AmE could enlighten us.