Quote Me Right

Let's talk proper quotes from a fiction perspective (I'm sure you can apply this to nonfiction, but that's not my focus).
I've seen too many people write dialogue using horrible inconsistent and, to put it simply, bad quotations. Not that it's hard to look this stuff up, but that's another story. Now let's get started.

When a new character speaks, that character, male or female or nonhuman, deserves a new line.
Incorrect: "How are you?" Mary said. "Stop asking me questions," John said. "You have to get ticked off by everything I say?"
Correct: "How are you?" Mary said. 
"Stop asking me questions," John said. 
"You have to get ticked off by everything I say?"

Don't use funky tags. The reason being is that usually it's redundant or plain wrong.
Incorrect: "What's the matter?" he asked. (This one is redundant. The question mark already tells us he asked a question).
"Nothing," she grimaced. (This one is bad because people don't grimace words, they say them.)
"Uh-huh," he retorted. (Again, redundant.)
Correct: "What's the matter?" he said.
"Nothing," she said.
"Uh-huh."

Quotes within quotes are single quotes.
Incorrect: "He said, "she's ugly.""
Correct: "He said, 'she's ugly.'"

When speech does not end the sentence, put the proper punctuation within the final quotation and continue lowercase, unless using a proper noun. There are situations where certain punctuation does not go within the quotes, but that does not usually apply to fiction writing.
Incorrect: "Kill her!" He said.
"Not yet" she said.
"I have nothing to say".
Correct: "Kill her!" he said.
"Not yet," she said.
"I have nothing to say."

Acknowledge the speaker prior to the end of long speech. This is especially important with more than two characters, where following who says what can be tricky.
Incorrect: "Well, I don't think we should go over there. That fence looks shaky and who knows what's behind them. My pop says they got alligators back there," Jim said. (It takes us two lines to find out who is speaking. Yuck.)
Correct: "Well," Jim said, "I don't think we should go over there. That fence looks shaky and who knows what's behind them. My pop says they got alligators back there." (Much better. Notice also how I don't end the sentence after Jim said, because the sentence naturally continues back into speech.)

Put action in the same paragraph as its attributed speaker.
Incorrect: "Don't talk to me," she said. He raised his hand to slap her.
"How dare you say that to me," he said.
Correct: "Don't talk to me," she said. 
He raised his hand to slap her. "How dare you say that to me," he said.

And a note on writing thoughts: Internal monologue (aka, thinking) should not be put in quotes. If you feel the need to separate it from the rest of your writing, put it in italics, though this is not necessary.

While some of these rules are grammatical, and breaking them is downright wrong, others are purely stylistic, but following them gives an sense of sophistication. Follow these rules and your fiction writing will, at least at first glance, look better.