There are three main groups of punctuation used widely in fiction: phrase modifiers, the Dots, and the Dashes.
These include an appositive phrase (that which doesn't affect the sentence whether it is or isn't there but are often fun to include just like this one,) into another sentence. This can be one of three ways: the em dash, parentheses, or commas. What you use will depend on what you're trying to do.
Em dash (—): More about this in the Dashes section, but when it comes to appositives, the dash separates the phrase from the sentence with more force than the other two options. It's like cutting the sentence in half with an axe.
Parentheses: Unless you're trying to make a joke or somehow make it seem like someone's whispering, you may not want to use this. Parentheses just sound like an inside joke. If that's what you're going for, then great.
Commas: This is definitely the most common choice, and for good reason. It creates a half pause, unlike a period (which creates a full pause) so it places emphasis on the phrase, but not so much it stops the action like the em dash or change the voice like the parentheses. Don't go trigger happy though. Commas in profusion can slow down the sentence so much I like to call it "pausing the reader to death." When you find yourself doing that, just split the thing up into separate sentences.
These are used to separate independent clauses, those things that can stand as whole sentences all by themselves.
Comma: Such a useful item this. In this instance, it's the cleanest thing to use. People skim over them quite naturally.
Colon: You rarely ever see this one except for when you're indicating a list of items. I did it at the beginning of this article. However, there is such a thing as a "jumper" where it's used to show a cause and affect relationship between the two clauses. "Mary reached for an axe: Richard decided he no longer wanted to be in the room." I wouldn't use too many jumpers though.
Semi-colon: If a comma is a half pause, and the period a full pause, than a semi-colon is a three-quarter pause. Using this is a stylistic choice, but it also has the added condition of separating two clauses only that have a lot to do with each other. "Mary reached for an axe; Richard decided he no longer wanted to be in the room."
Hyphen (-): This is the smallest line. It is never, I repeat never, used to break apart a sentence. That is the Em Dash's job. The hyphen joins words to each other or splits a word apart by syllables if the word continues over two lines or text. It has nothing to do with full sentences.
En Dash (–): There is a difference between the En and Em dashes. The En is about the length of a lowercase "n," made by putting a space on either side of a hyphen between two words. It's used as a replacement for "to" when you're indicating a period of time (1774–1776.)
Em Dash (—): The Em is the length of a lowercase "m," made by two hyphens (with no spaces) between two words. It creates an abrupt break to a sentence, particularly interrupted dialogue. "What are you—?"
Tilde (~): Just like a hyphen is never used for sentences, neither is a tilde. Tildes solely create accent marks for words. It is never used in place of a dash to break a sentence, or to break words like a hyphen.
Period: By far, this is the most important punctuation in the English language. When it doubt, use a period. It creates a full pause between sentences and finishes an idea. Sometimes nothing is more dramatic than a single period.
Exclamation Point (!): Use these sparingly. They can get old really fast and eventually loose all their effectiveness. Don't hurt me, but I get this impression when reading Pride and Prejudice. Way too many exclamation points for no reason for today's modern language. Unless someone really is screaming, don't use it. "Exclamation points are like laughing at your own joke." – F. Scott Fitzgerald. And never EVER use more than one at a time. Just…don't. Please. It hurts. Also, never double it up with a question mark (?!). Editors and publishers have been known to toss manuscripts with those. If you want to display surprise and puzzlement at the same time, there are better ways to show it than with double marks.
Quotation Mark (""): I am American. In the States, we use quotation marks to set off dialogue or a word. "Why would you do that?" End dialogue with periods, not commas. Keep in mind, other punctuation go inside the quotations, not outside, except semi-colons and colons. The only time you don't use quotations to set off a word is when the offset word is inside quotations. Then you use an apostrophe.
Apostrophe (''): When a word is inside quotations and you want to draw attention to it or set it apart, you use a set of apostrophes.
Spaces between Sentences: In the days of typewriters, double spaces between sentences where needed because of how the machine worked. Nowadays, word processing software automatically adjusts the spaces regardless of the font. I used double spaces for years, but I had to come to terms with the fact publishers no longer look kindly on them. Use a single space between your sentences. I know there is a great deal of contention about this and many people feel strongly about it.
Ellipses (…): These are ALWAYS three periods. Not two, not four, not five. Three. Just three. It's used in dialogue to represent speech that trails off to a stop. "I don't really know…"
Oxford Comma: This is the comma used in a list before the conjunction. For example, I have oranges, apples, and grapes. That comma after "apples" and before "and" is the Oxford comma. Much discussion has been made recently on the legitimacy of this simple punctuation. My husband, who teaches high mathematics at a university, says that mathematically speaking, the list is incorrect without the Oxford comma. That is because in mathematics, things listed in succession may not necessarily be together. Oranges may have nothing to do with the apples and grapes, so the Oxford comma is used to indicate the relationship or not. I personally think the Oxford comma perfectly fine and a wonderful punctuation mark. Lists just don't seem right without it.