Without quotations, you can't have dialogue. It seems simple enough -- every time a character speaks, just wrap quotation marks around every word they say. But where do the commas go? How should the periods be placed? There's nothing simple about using quotations in a story, because you've always got to add extra punctuation along with them. Are you doing it the right way?
The US vs. The UK
There are different styles of using quotation marks around the world, and therein lies the confusion. But on either side of the Atlantic, there are specific rules to follow -- and I love having specific rules to follow. Always embrace the rules of writing, because they're your friend.
The UK style of using quotation marks has varied over the years. It's quite common in British writings to use what we Americans call an apostrophe ( ' ) as what they call a single quotation mark, though in more modern Brit writing the double quotation that Americans are more familiar with has become increasingly common. For ordinary use, it's still acceptable in British writing to use the single quotation mark rather than the double. But that's not the only strange thing they do (with all due respect to the Brits, of course).
It's common in writing, in any part of the world, to break up dialogue sometimes. For example, I might write something like "I had a nightmare last night," Jade whispered, "about grammar chasing me around the bedroom!" But if I'm trying to be a British writer, what I've typed out is totally wrong.
Why? Because in interrupted quotations, British writers put that comma outside the quotation mark. The same sentence in the UK would read more like "I had a nightmare last night", Jade whispered, "about grammar chasing me around the bedroom." Now, to an American audience it's going to look totally incorrect, but in the British style of writing it's perfectly correct.
And that's the crux of it: are you going to punctuate your quotations in the American style, or the British style? You've got to make the decision, and you've got to know all the facts before you do so. You can be from the UK, but you don't have to write like it...and in fact, you might not want to. Let's examine the evidence.
Those who live in the United States, and as one of them I have nothing but respect for my countrymen, aren't generally very attuned to global culture. What I mean is, if you give an American a book with British punctuations, 9 times out of 10 they're going to think the book is filled with typos. So if you follow strict British punctuation rules, you could be alienating some of your US readers. You don't want that.
You might further consider that, currently, the United States leads the world in the amount of books it sells. In 2010, book sales totaled around $11.67 billion USD in the States -- a massive amount of money. In the same year in the UK, book sales earned about $5 billion USD. Of course, money isn't everything...but it's certainly worth considering. If the US is selling more books than the UK, to the tune of 2 to 1, it's probably a wise decision to follow US punctuation rules because books written in this fashion are clearly more prevalent than others.
Which, of course, brings us full circle: British quotation punctuation, to US readers, is going to look wrong most of the time. If you're marketing your book largely to a British audience, obviously you have to follow their rules. In short, these rules state that you should put additional punctuation (periods, commas, etc.) inside the quotation mark, unless you're writing an interrupted quote. When this is the case, put the punctuation outside the quotation. In the US, all punctuation always goes inside the quotation marks. Pick your path, and stick to it.
Whatever you do, don't make up your own rules. Follow the ones that are already in place...whichever side of the ocean you choose.