If you are writing within canon, make sure you stick to it.
Re-read the books, watch the movies again. Do a little research if you need to.
Half the time I spend writing, is time that is actually spent reading and making sure that I have the facts correct. Nothing is worse that misspelling a character’s name, or getting the core of their wand wrong(for those of us in the Harry Potter universe).
The difference between a good story and an amazing story is how much attention you pay to the little details.
If you write something completely original, then make sure you follow through with your ideas. A reader can only read what is on the screen in front of them, not what is in your mind. Allow the reader in by describing the different parts of the world that you have created. If you are creating a new character that is not part of canon, make sure you give them a unique personality, and let the reader know what that personality is. Bestow them with a name that suits this personality. Who are their friends? Who are their enemies? Where do they live? What colour is their hair? What type of food do they like to eat?
Having said that - don't list all the attributes of a new character within the first paragraph for a story.
E.g. My name is Elena and I am seventeen years old. I have an older brother names James and a younger sister called Sophie, but she is really annoying and we don't get on. I have long wavy hair which I hate because it gets frizzy, but I love my eyes because they are blue. I work at the local McDonald's. I don't get paid very much and my boss hates me, and makes it super hard for me to get my job done. What is his problem anyway?
This is frustrating, because it like reading a shopping list. Suddenly I know all about the character, and there is no mystery. What is the point to reading the story? I already know all about the character.
Something entirely different, but worth mentioning is the abbreviations that are used in descriptions of stories.
Take the time to learn the different abbreviations used in fan fiction. My list is by no means exhaustive, but here are some examples:
AU - Alternate Universe
Canon - follows the original story as set out by the actual author/creator of the characters
Drabble - a fan fiction that is written in 100 words or less
One shot - a fan fiction that is only one chapter or one scene in length
A/N - author's note (TIP: Never put an author's note in the middle of a chapter. It interrupts the flow of the paragraph)