TYPE 1: A quote that does not finish a sentence.

WRONG: "I think you should definitely go for it." Said John.
WRONG: "I think you should definitely go for it." said John.
WRONG: "I think you should definitely go for it" said John.
WRONG: "I think you should definitely go for it", said John.
RIGHT: "I think you should definitely go for it," said John.

Note how the quotation ends in a comma, and how the comma goes before the quote is closed. Also, the next word should be lower-case.

TYPE 2: A quote that ends with a question mark, but does not finish a sentence.

WRONG: "Are you sure you want to go through with this?" Said Sally.
RIGHT: "Are you sure you want to go through with this?" said Sally.

Again, the word after the quote closes is lower-case.

TYPE 3: A quote that ends a sentence.

WRONG: She smiled and said, "Well, if you insist"
WRONG: She smiled and said, "Well, if you insist".
RIGHT: She smiled and said, "Well, if you insist."

This is when you end with a period, inside the quotes.

TYPE 4: A sentence with a broken-up quote.

WRONG: "What I do in my free time," Frank started, looking Gerard dead in the eyes. "Is none of your damn business."
WRONG: "What I do in my free time," Frank started, looking Gerard dead in the eyes, "Is none of your damn business."
RIGHT: "What I do in my free time," Frank started, looking Gerard dead in the eyes, "is none of your damn business."

There should only be a single period. Also, only the first word of the sentence is capitalized. Think of it as just one sentence (which it is), but with added punctuation. All quotation marks are is punctuation, just like commas or apostrophes.

ADDITIONAL INFORMATION (thanks to mandy_croyance):
In regards to periods and their positioning around quotation marks, it should be said that the Americans conventionally place the period inside the quotation marks if the quotation comes at the end of a sentence regardless of whether the enclosed phrase is itself a complete sentence. The only exception made is for single letters or numbers, in which case the period follows the closed quote.
The British, however, place their periods logically: if the phrase within the quotation marks is a sentence in its own right, the period is placed inside the marks. If the phrase is not an independent sentence, the period is place outside of the marks.
Also, no preceding comma is necessary if the quoted phrase is not an independent sentence because neither text is parenthetical.

American: Brendon was upset that Ryan had called him an "aggravating, little brat."
British: Brendon was upset that Ryan had called him an "aggravating, little brat".

THAN VS. THEN
Than is used when comparing two things.

I am taller than you.
Three is greater than two.

Then is a word most commonly used to describe a sequence of events, to refer to a specific point in time, or to describe a case and consequence (there are other uses as well).

I walked outside, then turned back because I forgot my keys.
I was born in the 1990s; back then there were no iPods.
If you are unsure about your grammar, then you should read this.
If life ain't just a joke, then why are we laughing?

ITS VS. IT'S
Its is a possessive adjective (the possessive form of "it").

Have you seen my watch? Its battery is dead, and I'd like to replace it.

It's is a conjunction of the two words "it is," or "it has."

Your watch? I think it's under the table where you left it.
Hey, thanks! It's been a long time since I last saw it.

TO VS. TOO VS. TWO
To has a heck of a lot of uses, which I will not be typing up. If you'd like to see them, look here. Just a few:

Try not to make the same mistake again.
I'm moving to Alaska next summer.
I am falling apart to songs about hips and hearts.

Too is used to express "in addition," "extremely," to express an affirmative that contradicts a negative statement, or to say that something has been done in excess.

I too will be attending the concert.
I wasn't too happy when I found out that you were going. What if I say you can't come?
I am too coming!
You whine too much.

Two is a number. That is all.

Honey, this mirror isn't big enough for the two of us.

WHETHER VS. WEATHER
Whether is used to introduce an alternative.

You will do what I say, whether or not you like it.
Whether we go or we don't, it won't matter because we'll still have fun.

Weather refers to the climate conditions.

The weather is really bad today; first it poured, and now there's a blizzard!
It's 8:45. The weather is getting better by the hour. I hope it rains there all the time.
Our thoughts compressed, which makes us blessed, and makes for stormy weather.

DISCREET VS. DISCRETE
Discreet means subtle or unobtrusive.

I'm getting my tattoo in a discreet place so my mom won't see it and flip out.

Discrete means separate or distinct.

The house had two discrete parts: one for her work hours, and one for her recreation hours.
The story had three discrete sections: one from the point of view of each main character.

THEY'RE VS. THERE VS. THEIR
They're is a conjunction of the words "they are," and that is all.

These clouds we're seeing, they're explosions in the sky.

There means "at that place," "at that point in action," "in that respect,' etcetera (for a complete list of meanings, go here).

As razor sharp white teeth rip out our necks I saw you there.
This is me standing in the arch of the door, hating that look that's on your face that says there's another fool like me.
Be my breath, there's nothing I wouldn't give.
You should stop right there before you get hurt.

Their is a possessive adjective (possessive form of "they").

Let's follow the cops back home and rob their houses.

WERE VS. WE'RE
Were is the plural past tense form of the verb "to be," OR a subjunctive verb (for more about this use, see the MISCELLANEOUS section).

Walk away to save your face, you never were an actor.
If I were your English teacher, I'd have to kill myself.

We're is a conjuction of the words "we are."

Mama, we're all full of lies. Mama, we're meant for the flies.

YOUR VS. YOU'RE
This one deserves a special heading:
"YOUR STUPID." MY STUPID WHAT?
Your is the possessive form of "you," singular and plural.

And we could settle this affair if you would shed your yellow, take my hand.
Where is your boy tonight? I hope he is a gentleman.
I wrote a goodbye note in lipstick on your arm when you passed out.

You're is a conjunction of the words "you are."

I'm just a notch in your bedpost, but you're just a line in a song.
You're holding on to your grudge.

LOSE VS. LOOSE
Lose is a verb that means "to misplace," or "to suffer the deprivation of," or "to not win."

Last chance to lose your keys.
If I sleep with you, I could lose my job.
I will never enter a 'who's-a-bigger-whore' contest against Pete Wentz, because I would definitely lose.

Loose is an adjective that means "slackened," "free from restriction," "sexually promiscuous or immoral," "not strict," etc.

Gosh, if those pants get any more loose, they might fall off!
My hair always falls in my face when it's loose.
Pete Wentz is pretty loose--he's slept with most of his friends.
The rues of this community aren't at all loose--if your grammar sucks, your post will be rejected.

WHOSE VS. WHO'S
Whose is either an adjective as the possessive form of "who," "which," or means "the one or ones belonging to what person or persons."

And all the girls whose lips couldn't move fast enough, sing until your lungs give out.
I'm a fool whose tool is small; it's so miniscule it's no tool at all.

Who's is a conjunction of the words "who is."

I'm just a boy who's meant to sing this song.
Preach all you want, but who's gonna save me?
You're the one who's always bruised and broken.

WHETHER VS. IF (thanks to mandy_croyance)
Whether is applied in situations where there are two options, and often implies an "or not".

Travis wondered whether William would wear his bandana today [or not].
Whether he wore it around his thigh or head didn't matter.

If is applied to a conditional circumstance, and usually includes some causation.

If he wore the bandana, Travis would kiss him.

LITERALLY
This word is the opposite of figuratively, and means "without exaggeration or inaccuracy." This word is misused a lot, and turned into something else. Examples of misuse (thanks to draicana):

"I was literally over the moon!" Oh really? How was the view?
"I was literally blushing!" You can blush metaphorically? Neat trick!

HYSTERICAL VS. HILARIOUS
"Hysterical" is often wrongly used in the place of "hilarious." Hysterical means "uncontrollably emotional," whereas hilarious means "arousing great merriment; cheerful." Therefore, when you say a joke is hysterical, you are really saying that the joke is uncontrollably emotional. Example of misuse (thanks to draicana because she is amusing):

"I heard this joke the other day, it's hysterical!" Really? Is it blue too? Or pretty? Or angry?

LINE BREAKS
We all know that in books, there are no spaces in-between paragraphs--it just goes right to the next line, and indents to indicate the start of a new paragraph. But this is not proper online, because it makes our eyes cross and/or bleed.
WRONG:

    Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Maecenas feugiat consequat diam. Maecenas metus. Vivamus diam purus, cursus a, commodo non, facilisis vitae, nulla. Aenean dictum lacinia tortor. Nunc iaculis, nibh non iaculis aliquam, orci felis euismod neque, sed ornare massa mauris sed velit. Nulla pretium mi et risus. Fusce mi pede, tempor id, cursus ac, ullamcorper nec, enim. Sed tortor. Curabitur molestie. Duis velit augue, condimentum at, ultrices a, luctus ut, orci.
    Donec pellentesque egestas eros. Integer cursus, augue in cursus faucibus, eros pede bibendum sem, in tempus tellus justo quis ligula. Etiam eget tortor. Vestibulum rutrum, est ut placerat elementum, lectus nisl aliquam velit, tempor aliquam eros nunc nonummy metus. In eros metus, gravida a, gravida sed, lobortis id, turpis. Ut ultrices, ipsum at venenatis fringilla, sem nulla lacinia tellus, eget aliquet turpis mauris non enim. Nam turpis. Suspendisse lacinia. Curabitur ac tortor ut ipsum egestas elementum. Nunc imperdiet gravida mauris.

Online, we skip a line between paragraphs, and do not indent. It is much easier to read this way.
RIGHT:

Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Maecenas feugiat consequat diam. Maecenas metus. Vivamus diam purus, cursus a, commodo non, facilisis vitae, nulla. Aenean dictum lacinia tortor. Nunc iaculis, nibh non iaculis aliquam, orci felis euismod neque, sed ornare massa mauris sed velit. Nulla pretium mi et risus. Fusce mi pede, tempor id, cursus ac, ullamcorper nec, enim. Sed tortor. Curabitur molestie. Duis velit augue, condimentum at, ultrices a, luctus ut, orci.

Donec pellentesque egestas eros. Integer cursus, augue in cursus faucibus, eros pede bibendum sem, in tempus tellus justo quis ligula. Etiam eget tortor. Vestibulum rutrum, est ut placerat elementum, lectus nisl aliquam velit, tempor aliquam eros nunc nonummy metus. In eros metus, gravida a, gravida sed, lobortis id, turpis. Ut ultrices, ipsum at venenatis fringilla, sem nulla lacinia tellus, eget aliquet turpis mauris non enim. Nam turpis. Suspendisse lacinia. Curabitur ac tortor ut ipsum egestas elementum. Nunc imperdiet gravida mauris.

DIALOGUE
Every time someone different begins to speak, a new paragraph must be started (for correct punctuation in quotations, see the first section).
WRONG:

"Thanks for the memories, even though they weren't so great," Pete said spitefully. "He tastes like you, only sweeter," Mikey replied with just as much venom. A long silence followed, and then Pete spoke up again. "One night, and one more time."

RIGHT:

"Thanks for the memories, even though they weren't so great," Pete said spitefully.

"He tastes like you, only sweeter," Mikey replied with just as much venom.

A long silence followed, and then Pete spoke up again. "One night, and one more time."

Bahahaha, I'm so lame. *ahem* Anyway, if someone is speaking for a long time, like they're telling a story, and change the topic so you'd have to start a new paragraph, you do not close the quotes, but you have to open them again in the next paragraph.
WRONG:

When I was a young boy, my father took me into the city to see a marching band. He said, "Son, when you grow up, would you be the savior of the broken, the beaten, and the damned?"

"Will you defeat them? Your demons? And all the non-believers; the plans that they have made? Because one day I'll leave you--a phantom--to lead you in the summer. To join The Black Parade."

RIGHT:

When I was a young boy, my father took me into the city to see a marching band. He said, "Son, when you grow up, would you be the savior of the broken, the beaten, and the damned?

"Will you defeat them? Your demons? And all the non-believers; the plans that they have made? Because one day I'll leave you--a phantom--to lead you in the summer. To join The Black Parade."

MISSPELLED WORDS
Guys, it's DEFINITELY. Not definetly, defanitly, defenitely, etc. D-E-F-I-N-I-T-E-L-Y. But you should be using spellcheck anyway, so this shouldn't be a problem.

TENSES
Generally when you are writing something, you're going to make a decision about the tense. Usually, it will be either present (ex: I walk over to him and say hello) or past (ex: I walked over to him and said hello). Be aware of your tenses, and make the conscious decision to use one for your story. The tense you choose isn't so important, but sticking with it is. Please, make sure your tense is consistent throughout your story.

*NOTE: Please excuse the insane amount of MCR/FOB/Placebo/Brand New lyrics I used to demonstrate my points, as well as the random OTP-pimping and Pete Wentz referencing. I had to have a little fun, amirite?

LOL I just read this over and realized I made one of the mistakes on the list. >.< TWAS A TYPO I SWEAR! That's why everyone needs a beta. xD

If you have any questions, ask! I hope I helped. :)