Free Indirect Discourse is the original term, being a direct translation from the French discours indirect libre, but that doesn't get you much further. And least helpful of all is Free Indirect Speech, because most of the time we don't use the term for stuff which was said aloud. (Does it make more sense in French, given that they don't routinely use speech marks in fiction? A question for another day.) But we're stuck with the name, and it's not really as vague and alarming as it suggests: quite likely you've been doing it all along - you just didn't know it has a name. But in case it's all new to you, let's start at the beginning.
Think of your characters speaking: if you want to convey the actual words that someone said, without quoting them directly, then you use what's called reported speech:
If you have an external, knowledgeable narrator, and a narrative in third person, then the shift of tense and person is obvious: John said, "I don't believe you," becomes John said he didn't believe her. Don't becomes didn't, I becomes he and you becomes she.
If you have an internal, character-narrator, and a narrative in first person, it works just the same: "You can't leave me like this, alone on Rockall!" I yelled becomes I yelled that she couldn't leave me like that, alone on Rockall! The shift of tense and person is just the same: in the dialogue can't becomes couldn't, and you becomes she.
What Jane Austen realised, for which we should all be profoundly grateful and, unquestionably, put her on the £10 note, was that you can do the same with thoughts: reported thought rather than directly quoted thought, if you like. Just as with speech, the clue is that the tenses fit with the normal narrative tense, but the voice is the character's. So, if your straightforward narrative with directly-quoted thoughts and speech was this:
Emily was one of those people who hated confronting liars. She put down her coffee and thought, he's a bastard! He's obviously lying! She picked up her coffee again. "How sweet of you to be so honest."
then free indirect style integrates thoughts and speech into the narrative:
Emily was one of those people who hated confronting liars. She put down her coffee. He was a bastard! He was obviously lying. She picked up her coffee again and said how sweet it was of John to be so honest.
Notice how, once we're in free indirect style, we lose the need for a "she ... thought". The fact that we're in Emily's point of view, and these words are in Emily's voice, is enough for us read it as a direct representation of her thought. And because the tense and person remain the same as that of the narrative, there's no abrupt jump from narrator' consciousness to Emily's consciousness; instead there's a slide from the voice of the narrator dominating the narrative, towards the voice of the character dominating it, depending on where we are in psychic distance.
Notice, too, how smoothly we move from the narrator's voice - telling us about Emily's dislike of confronting liars - into the narrator telling us about a physical action of Emily's, which gets us closer in psychic distance. We're then nicely placed to slip inside Emily's head with the reported thought of "he was a bastard".
On the other hand there are moments when the fact that we can slide (not jump) between voices means the reader needs a little help. In the directly quoted version, readers are used to associating an action with a bit of speech, without the need for a speech tag. We know that her saying "it's sweet of you" doesn't just run on from the thought because it comes after "she picked up her coffee". In the free indirect style version we probably do need the "she... said", to make sure we don't read "how sweet it was" as more thought following on from "he was lying", but as something said aloud. Leave it out, and you're in Wolf Hall territory: as I was saying here, it's wonderful, but some readers will find it too confusing to follow the story easily.
But I do see why Mantel took the fluidity of free indirect style to that extreme, such is the joy of how you can move freely from the narrator's consciousness into a character's, by using voices as part of the narrative, without having to explain it all, or expand things to the "real-time" of full dialogue. There's more on this in Blow by Blow; for now, just consider a version of the scrap from that post, as a reason to learn to use free indirect style:
"How long can you stay?" I asked.
She slung her jacket over the back of a chair. "My bus doesn't go till six."
"Good. I'll put the kettle on."
We sorted out the business of coffee - when had she gone decaff-only? - and I waited until the kettle had boiled and the dog been let out into the garden before I said, "Did you get my letter?"
Notice how free indirect style works just as well with a narrator who is also a character, and is therefore narrating in first person: when had she gone? is the free indirect version of the direct thought when did she go?. But notice, also, how much less scope there is to work this way if your narrative is already in present tense. How do does the reader know when the character-narrator is transmitting the charactor-actor's thought, if you don't have the shift into the past tense? This is one of David Jauss's reasons for finding present tense, as a narrative tense, very limiting, which he explores in On Writing Fiction, and I've blogged about the pros and cons of past and present tense here.
Another plus of free indirect style is that with luck you can fight off your editor's demands that directly quoted thoughts have to go in italics, by shifting into reporting them. In the days when a character's thoughts were often put in " ", it was more obvious whether the thought was directly quoted, or being reported. But nowadays on the whole only things said aloud get " "s, and I think the italics thing comes from nervousness that without some kind of marker readers won't get that this is the character's thought. But that's daft: readers have had decades of experience at picking up the cues, and as long as you write it right, they're quite capable of reading it as you want them to without having to stop and work it out. As far as I'm concerned, putting thoughts into italics is an unnecessary doubling-up of effects: the lazy or insecure writer's/publisher's way of keeping the reader on track. I want italics for other things more difficult to differentiate, and if you use free indirect style, you don't need them for thoughts: you can have all the voice and energy of the character's thought, but as part of the run of the narrative.
And, of course, if you're working with a knowledgeable narrator, to whom you've given privileged access into more than one head, then using free indirect style helps you to slide smoothly out of one point of view and into another. If standard realist narrative with directly quoted thought is like this:
Andy Pandy looked at the bears with an indulgent eye. I don't like seeing bears all growly and cross, he thought. But I do like seeing them when they're jolly and I can play with them. He jumped down into the pit.
and the free indirect version is this:
Andy Pandy looked at the bears with an indulgent eye. He didn't like seeing bears all growly and cross, but he did like seeing them when they were all jolly and he could play with them. He jumped down into the pit.
Then how do you move of point of view? Just go via the narrator, and make the most of the different voice-y-ness of the narrator and the different characters:
Andy Pandy looked at the bears with an indulgent eye. He didn't like seeing bears all growly and cross, but he did like seeing them when they were all jolly and he could play with them. He jumped down into the pit, oblivious to Nanny Jilly's cries. She, by contrast, didn't trust the bears an inch. They were dirty, and greedy, and not at all the kind of playmates a nicely-brought-up boy-doll should have. And if Mrs Pandy ever asked her about it, that's what she'd say.
And if your narrator is also a character? As ever, it's clearest if you think of your narrator as looking at themselves as a character from a little distance.
When I was a boy, before the unfortunate incident in which Nanny Jilly had her head torn off by a grizzly, I looked at bears with an indulgent eye, as all little boy-dolls do. I didn't like seeing bears all growly and cross, but I did like seeing them when they were jolly and I could play with them. Nanny Jilly disapproved, of course; she thought they were dirty and greedy, and told my mother so.
And notice how lightly the sense of Nanny Jilly's voice is touched in, just using "dirty and greedy" in what's otherwise adult-Andy's narrative voice. That's another joy of free indirect style: how you don't have to either Show/Evoke a directly quoted thought to us, or stick to the narrator Telling/Informing us about the thought. You can choose how strong the colouring is and how long it goes on for. Free indirect style can help to make your Telling Show-y.
Free Indirect Style isn't just a basic narrative technique, of course, it's also central to the business of storytelling in prose or poetry, and it's one of the biggest advantages we have over the playwrights and scriptwriters. Is it Austen’s or Emma’s voice that declares that "Mr Knightley must marry no one but herself!"? The answer isn’t quite "both": this isn't two people speaking in unison. The subjective voice and consciousness of Emma, and Austen’s voice and consciousness as the knowledgeable storyteller, have both moved into the gap that usually separates character from narrator. "We inhabit both omniscience and partiality at once," James Wood puts it in How Fiction Works, and, if only intuitively, the reader does feel this double-consciousness. But the merging of two perceptions into a single expression reinforces their actual difference: each is more vividly itself.
What's more, the bigger the gap between the narrator's voice and point of view, and a character's voice and point of view, the more irony becomes a part of the storytelling, because irony depends on us holding two different understandings of a single statement, and feeling the gap between them. I won't go on here, but if you know Emma, you'll know that lots of characters, as well as the narrator, talk about how ghastly Mrs Elton is. By contrast, Mr Woodhouse's selfishness is never spoken of explicitly. His solipsism and blinkeredness is ultimately just as big a threat to people's happiness, especially Emma's, but Austen conveys it purely by quoting and reporting his voice and actions, colouring the narrative without commenting on it. Nor is he ever challenged in the story: the other characters just tacitly circumvent or avoid the obstacle that is Mr Woodhouse, and so how the story is told is integrated with what the story is telling. And all with a few changes of tense, and person.