Contractions are shortened forms of words and phrases, and are used in both speech and writing. An example of a contracted word would be "can't" from "cannot." A contracted phrase might be the contracting of "let us" to "let's." Regardless of whether a contraction is used in a letter, academic prose or professional writing, the rules governing contractions are always the same. In fiction, however, there's a little bit of leeway.
General Rules with Contractions
The most basic rule about contractions is that an apostrophe is used in place of all omitted letters. For example, to create the contraction "don't," the phrase "do not" has been squeezed into one word, and the "o" in "not" has been replaced by an apostrophe. An apostrophe can also replace more than a single letter: when forming "can't" from "cannot," the apostrophe replaces both the second "n" and the "o."
Advantages and Drawbacks
Contractions can make writing and speech sound more friendly, and they certainly make all forms of language more efficient, but they also have the drawback of adding a potential air of informality to whatever type of discourse is being used. Some language experts claim that contractions are inappropriate for formal or academic writing because of the casual tone. In fiction, however, informality and the comparative formality are strategies a writer can use when telling a story, and contractions are an effective tool.
Contractions in dialogue often make the speech read as more natural sounding and mimic how people actually speak, which helps to keep the reader captivated by the story. This effect can even be heightened by using contractions to nuance regional accents and dialect. However, a word of caution: using contractions for accents and dialect, while potentially accurate, can be difficult to read if the dialect is thick.
Using contractions in fictional narration can be just as useful as in other applications. They are efficient and create a conversational tone that is often easy to read. However, your narrator is a character, and when dealing with narration you must consider whether or not your narrator would use contractions, and which kinds and how. Furthermore, the same dangers that exist with dialect in dialogue exist with narration. Contractions can either add a richness and sense of culture to the writing or, like in James Joyce's "Finnegan's Wake," they can add to the confusion and render the story nearly unreadable.