Article: While some canon characters have vague pasts that can be manipulated, a frequent and recognized (although not compulsory) trait of a Mary Sue is to be related in some way to a canon, especially one who has a strongly established past already. Your readers may find it hard to believe that the canon character has a sister he never mentioned or a son she doesn't remember. Your original character should not constantly be the center of the universe.  Let the other characters have moments away from your new character where they don't talk or think about the new character. Remember why they're there. Your readers want to read about the canon characters, that's why you're writing a fan-fiction. Make sure that your chosen name fits in with the fandom. For example, don't have a Harry Potter character called Trixiebella Arwen, or a LOTR elf called Jane. There are plenty of sites online where you can research names to make sure that they fit with your chosen fandom.  Baby name sites are a good start, but don't go mad. Names like "Angelica Rowanna Marybelle Devenish" are ridiculous and not realistic. Don't use traits like hair color or facial features either, as most children are named at birth. Don't use your own name, or a variation of it. This just screams "Mary Sue" to readers.
What is a summary of what this article is about?
Avoid making your character related to a canon character. Make your character part of the ensemble cast, maybe even a very small part. Let the canon characters share the spotlight with your character. Pick a realistic name.