Character Development
What is a Mary Sue you may ask? A Mary Sue (or Gary Stu) is a fictional character, usually female and especially in fanfic, whose implausible talents and likeableness weaken the story. In other words, a character who is clearly the author's alter ego and therefore incredibly perfect, incredibly beautiful--often with unusually colored eyes/hair, incredibly talented--often gifted musically and magically, has a tragic past, and is either related to or beloved by one or more of the stories characters.
The main thing you can do to prevent Sueishness is to give your character flaws. Some authors think that making a character clumsy or something will keep them from being a Sue. This isn't true. It has to be something more major. Like your character has a big ego, is a coward, not athletic or whatever.
Most teenagers are zitty with bad teeth or frizzy hair or are overweight or something. You can't have your perfect haired, flawless skinned teen with an hourglass figure. It just doesn't happen. Well, unless they're a daughter of Aphrodite.
Also, to keep a character realistic, you need to give them a life. A past, a family, hobbies, etc.
I mean, you can't just take a character and throw them at a monster. What has your character been through? They must have had a family at some point. You can't just kill their mother and then have them forget it as they go off to fight the world, you know? They should remember their family. Even if it wasn't the best family life there should be a moment they look back on often. What is your character's history?
Another thing, hobbies. Everyone, and I mean everyone, has something they are passionate about. Like myself, I am obsessed with photography and writing, my friends are into sports, and well, what does Bella do? Bella likes riding motorcycles I suppose.
Your character should also develop over time or after a traumatic event, like Harry Potter. Harry started out thinking he was a muggle and by the end of the series was one of the most respected wizards to walk the earth. On the other hand, Bella was the same after the James incident, but we don't talk about paper characters like her.
Now, when we're talking about fanfiction especial we have to talk about Out of Character (OOC.) A character who is usually shy can't suddenly become witty and sarcastic before going back to shy. And when you're using another persons character this is especially important, Draco can't suddenly become a sweet sensitive young man because that's not who he is. The only exception I can see to this is if something happens to them that changes their character (as said above.) But you can't just say at the beginning of your story "Oh yeah, and Draco's the sweetest person alive now." and never say why.
POV
PICK A POV AND STICK TO IT.
Don't constantly switch point-of-view throughout a chapter, if you absolutely must change POV start a new chapter. Make sure your character's voice is heard in their POV, as in if you're telling the story in first-person, and your character is a pessimist, the book should have a negative feel to it. Also, avoid retelling events from multiple POVs. I find it annoying to read:
Annabeth POV: "Hi Percy!" I said.
Percy POV: "Hi Percy!" Annabeth said.
Recap
There's a really great character helper on Rick Riordan's website. But if you want a quick way out, here are some things to remember about your new character.
-Flaws in personality
-flaws in appearance
-hobbies
-history
-talents
-Point of View. How does your character see things? Critically? Optimistically?
These things will help bring your character to life.

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