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You do it in chunks. Let the character explain that he is the right one for the job because he has done this thing in the past. Let another character a chapter later point out that they knew this c...
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#4: Attribution notice removed
Source: https://writers.stackexchange.com/a/34310 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#3: Attribution notice added
Source: https://writers.stackexchange.com/a/34310 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#2: Initial revision
You do it in chunks. Let the character explain that he is the right one for the job because he has done this thing in the past. Let another character a chapter later point out that they knew this character for years and can always trust that this character will get it done. Let him share something at the fireplace from his past in exchange for information about the other character. Another chapter later you see this character do something incredibly good - another character murmurs that it must have taken him years of hard training to achieve this mastery. You don't want to simply tell the reader in a long monologue, but you need to show it somehow. As long as you don't dump the information on the reader and instead introduce it whenever it's relevant this is fine - it doesn't matter whether the character explains it themselves or another character or someone just thinks they know something. And you should only ever show your reader the important parts of the backstory. It doesn't matter how many sisters the character had - except for when finding one of them is his motivation, or they collectively taught him something, or they are individually important to him or the story.