Perspectives:
Before writing a story, it's important to consider carefully what point of view you're going to use. Most of us know the kinds of points of view available: first person, second person, and third person, which can either be omniscient or limited. Writers, as a rule, know these perspectives. But creative things can be done within the limits of these points of view.
Most modern fiction writers choose between first person and third person limited. Third person limited is like in Harry Potter, wherein the narrator follows the perspective of one or more important characters to tell the story. I, personally, prefer first person because I can use it to get deeply into the character's point of view, though a lot of writers can achieve a similar effect with third person limited. If you're not sure which you'd prefer to use, experiment with it. See what sounds better. If you're trying third person, and it doesn't feel right, try first person.
Something New:
Experimental and interesting approaches are available with all of these perspectives. With my current series of novels, I'm following the example set by Kathryn Stockett, author of The Help. In that popular novel, three women, a white woman and two black women, take turns being the narrator. The reader gets a more complete understanding of the situation because he/she isn't limited to just one set of eyes or thoughts. The narrator in each case speaks in the voice of the perspectival character. Currently, I am writing first person, alternating between the male character's and the female character's voices. It's not a common technique, but I enjoyed using it to fully explore both an insecure, introverted woman and an insecure, introverted man. I have yet to find out what kind of reception I will receive from the publisher since it's not a common technique.
The more common approach to this kind of shared narrative would be 3rd person. The traditional, and somewhat outdated, way of writing would be to assume an impartial voice of a narrator who knows everything, but fewer and fewer writers use this approach because readers prefer the experience of feeling what the character feels rather than just hearing what they do. It's easier for the writer to show rather than tell when viewing the story through the eyes of a character. 3rd person limited allows the flexibility of shifting perspectives between main characters and even minor characters involved in events critical to the story. One danger with too much head jumping is that it's easy to flit back and forth in the middle of a chapter and, more problematic yet, a single paragraph. Readers can find a dizzying amount of head jumping disorienting, and publishers take this as a clear sign of a novice writer. I read a romance novel recently in which the meeting of the man and the woman was like a pingpong game, where each event was told from one perspective then the other in rapid succession, so there was no mystery, no tension, and no stability. It's usually best to limit head jumping to between sections of a chapter or, better yet, a shift between chapters.
Best of all would be as with Harry Potter, to focus on one single perspective for the entire story. Some stories can't easily be told this way. However, remember that the reader still sees some chapters through Voldemort's eyes because Harry is in his head or having a dream at the time. The reader still gets multiple perspectives by following Harry around.
Experimenting:
There are other techniques one can use with point of view that would be even more experimental. I have read short stories told through the 2rd person perspective, one usually reserved for instruction manuals. The most well-known type of 2nd person story is Choose Your Own Adventure books, in which the reader participates in the story, choosing what the characters will do. But this is not the only use for the 2nd person perspective in fiction. What could happen when the "you" addressed in the story actually does something like commits a murder and has to hide it? Or when the "you" in the story is a detective or a romantic lead? This could be either a narrative or an instruction manual, a how-to of crime, crime solving, or whatever. I've seen this technique used, but it would be difficult to pull off well. Examples are listed here.
With third person, the narrator is assumed to be trustworthy because he's simply a voice telling the story. Why would he lie? A truly good author writing in 3rd person limited or 1st person can achieve a higher level of art with an unreliable narrator. Somehow, either through switching points of view or through some other means, the writer is able to indicate to the reader that his narrator is untrustworthy, that the narrator has a clear bias or is telling the story in such a way that it shouldn't be believed at face value. In Wonderlandiful World of the Ever After High trilogy by Shannon Hale, the narrator first interacts with a character in a way that shows the narrator to be a character in his own right, and his descriptions suspect. Then the true narrator goes insane. His words make less and less sense as he's consumed by the Jabberwock's magic. Maddie, daughter of the Mad Hatter, takes on the role of narrator and quickly shows her own biases and thought processes contrasting with the reality of the story. When her father is in trouble, she doesn't even want to talk about what's happening. At one point in the narrative, Kitty, the daughter of the Cheshire Cat, takes over as another narrator and blatantly starts to make things up because what's actually happening is boring. This kind of unreliable narrator enhances the intrigue and level of art in the story if done well, though it can confuse the reader if done poorly. Here is an article with examples of novels with unreliable narrators.
Sometimes, an entire story can be inspired by points of view. I have written fun short stories from the points of view of a McDonalds paper cup, the evil fairy in my own version of "Sleeping Beauty," and from the point of view of the frog in "Frog Prince," among others. Sometimes, all it takes to make a story fresh is to see it from another point of view. Disney with "Maleficent" and "Descendants," Broadway with "Wicked," and so many others have made this practice more common, though there is so much more territory left to explore. One of the most interesting experiments in perspective was written by Orson Scott Card. Multiple decades ago, he wrote Ender's Game from the point of view of Ender, an earnest young man in a military academy set in space. About a decade ago, he retold the same story in Ender's Shadow from the point of view of Ender's subversive sidekick, Bean, who experienced the same events in an entirely different manner. If you're interested in perspective hopping and what it does for a story, read those two novels back to back.
Heightening Drama:
One of the things to consider with point of view, especially a shifting point of view, is which character to follow at any given time. Which character's perspective will heighten the drama? If there are two characters entering a situation, it may be more helpful to follow the perspective of the newcomer because the reader, too, will be new to this situation. That character can stand in as the reader in their exploration of that situation. For example, we enter the Wizarding World through Harry's eyes. If one character is really hurting but not showing it, it may be interesting to get inside her/his head, so we can experience the whole depth of the character's pain. Orson Scott Card points out that too many tears by the main character can actually turn a reader off. Sometimes, it may be best to follow the character who isn't suffering the most, so readers can watch the suffering character's heroic struggle. The best way to figure out which character would be best to follow may be to write both perspectives and see which is more successful, which does a better job of enhancing the plot and meaning.
The point of view of the narrator and main character are your reader's lens through which they see the entire story. If the narrator's perspective on the main character is engaging, convincing, and clear, the reader is far more likely to follow your books and listen to your entire story and its sequels. If the narrator's voice is humorous, endearing, clever, or in some way unique in a good way, you'll probably get a fan base who will follow you to the ends of the earth and beyond. That is the power of point of view.