To begin with, be aware that there are two general ways that quotes can look to the end user. The first is a straight up-and-down quote which looks like this - ". That quote has no difference between the starting quote and ending quote. So if your book had the line:
Joan said, "This is a lovely day."
The quote mark that starts the speaking section and the quote mark that ends the speaking section are exactly the same.
It is far better and proper to use curly quotes - quotes that show clearly where the speaking begins and ends. It's a typographical standard and it's easier on the reader's eyes to have the distinction be absolutely clear. So that would look like this -
Joan said, “This is a lovely day.”
If you look carefully you can see that the left quote curls counter-clockwise from the top, while the right quote curls clockwise from the top. Every commercial word processor including Word should have the option to do these curly quotes.
The rule for quotes, in the US, is that they go around what is said, including any end punctuation. There is always a space before the starting quote.
Incorrect: Joan said,“This is a lovely day.” (no space between comma and starting quote)
Correct: Joan said, “This is a lovely day.” (a space between comma and starting quote)
There should always be a comma between the "said" verb and the phrase being said.
If the person speaking then quotes someone else, the phrasing should be set off with SINGLE quotes. That way it is clear what part is said by the first speaker and what part is being said by the referenced speaker.
Joan said, “Mary came by this afternoon and she said to me, ‘This is a lovely day’ and then walked away.”
The use of single quotes within the phrase helps make clear what Mary said.
It can look confusing when you have quotes up against each other, as in this construction:
Joan said, “Mary came by this afternoon and she said to me, ‘This is a lovely day.’”
The ending single quote (from Mary's statement) runs right into the ending double quote (from Joan's statement) and this can create a confusing blur on the web. In print books the standard is to leave them touching like that, because the auto-spacing in a book should then create a slight space between the two that makes it clear one is a single quote and the other is a double quote. On the web that spacing is far less clear and sometimes writers artificially insert a space between the single quote and the double quote to help make it clear what each one is, like this:
Joan said, “Mary came by this afternoon and she said to me, ‘This is a lovely day.’ ”
While not quite standard practice, it is accepted for clarity reasons.
It's good to glance at a style manual to ensure your use of quotes is correct. It's an easy enough thing to learn to do properly, and since quotes are used so often in most novels it can becoming a maddening annoyance to readers if it is continually done incorrectly. You want to avoid all angst!
If you're currently not consistently using curly quotes, read about Fixing Curly Quote Issues
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