You can presume a little knowledge on your readers' part and spend a little less time describing commonly-known elements. The characters are not your own and you have to work harder to keep them in-character, otherwise people are not going to enjoy the story, But aside from those details, writing a fan fiction is no different from writing an original concept story. All the same technical rules still apply.
Yeah everyone has said everything I could probably say, lols.
I do have some general advice though.
But the best thing to do is know what your writing. If you're writing comedy, you can probably get away with a lot more OOC than other types of fanfiction.
Also, really, just keep in mind of the universe and during what part of the story the fanfiction is being placed in.
I also find it more forgiving to use Japanese words in Japan. If it takes place in Japan (not Japan inspired, mind you)I find the offense totally forgivable. However, I'd still be light on the usage.
Be careful with how you ship characters to, especially if there are storyline pairings. You may need to make up reasons for why the couple didn't really work out or something. However, I really stop giving fucks when it comes to couples, because you can ship anyone, and somebody will find someway to hate you.
Oh, but one word of advice, don't let people ever let you down because you write fanfiction. It isn't something people should really be looking down upon, so ignore people who say you shouldn't write it or that it's bad. That is the best piece of advice I can give you.
Sorry to butt in here but the easiest way I found to write a fanfic is to create you own world with the universe (guidelines) of the mainstream story. It's easier and allows for more freedom as you don't have to worry about maintaining the appearance (personality, etc) of the already established characters. So then it truly does became an original story just within the rules of the ficti0onal world your writing through. Hopefully this helps.