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Sometimes it can be helpful to use your plot to extrapolate what the characters who are involved in it are like. Let's say you're writing a story about a long sea voyage. Right away, that tells you...
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#3: Attribution notice added
Source: https://writers.stackexchange.com/a/1509 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#2: Initial revision
Sometimes it can be helpful to use your plot to extrapolate what the characters who are involved in it are like. Let's say you're writing a story about a long sea voyage. Right away, that tells you that the main character has some sort of reason for being on a sea voyage. And once you know what that is, you'll know a few things about who this character is. If your character is going out to explore the world, that's going to indicate certain things about his or her personality (adventurous) and possibly the resources he or she has access to (the money and supplies needed to mount such an expedition, including the ship). Then you can go a little deeper into why this character is looking to explore the world, which will suggest still more about the character. Is this a grizzled veteran sailor looking for one last chance to discover something and gain a place in history? Or perhaps a naive noble who thinks going to sea will be a fun adventure? Or maybe a sailor hoping to strike it rich and make a better life for his or her family back home? That's only a few of the possibilties, but you can see how each reason for wanting to explore at sea would suggest a different background, social status, and personality for each of these characters. Of course, just deducing character traits from the plot can lead to boring, stereotypical characters. So once you have the basics, play around with it a bit. Ask yourself "What would happen if this person was A instead of B?" Doing that a couple of times and picking the results that lead to the most interesting character while still giving him or her a reason and capability to do what your plot requires. As a couple of other people have already said, don't add quirks just to add quirks. You will probably want to figure out the particular ways your character show certain emotions or what he or she does when there's not much else to do. But there should be a reason that makes sense in the story for everything that happens. The fact that your character is a terrible trumpet player isn't important unless your character has a plausible reason to play the trumpet or talk about playing the trumpet during the course of the story. The character's lack of trumpet playing skills may reveal how she has never really finished anything she started before or how he had a bad relationship with his father, but you still need a logical reason for it to come up in conversation or for the character to play the trumpet, let alone bring it on a sea voyage.