Well, okay, first off, there's no rules. That's the glory of fanfic; it is done for love and distributed for free, and with all that comes the freedom to do whatever the heck you like.
There are a lot of reasons to write, including but not limited to "fix fics" (when a writer takes something that really annoyed them -- like the end of Mass Effect 3 -- and writes an ending they like better), or the inclusion of other voices, or random fun, or porn, or to practice writing in general or show off or try out techniques you might not want to risk in a more "serious" work.
But if chief among your reasons is the desire to be read, then there are a few things that it usually works better to follow:
1. Attend to canon. The very act of fanfiction on an existing intellectual property produces the first paragraphs of an implicit contract with the reader. If you don't know this concept, think of it this way; if you dress a book in autumnal colors and decorate it with people with long hair and swords and name them "Elisival Half-Elven" and "Tanis the Horse-Master" the reader shouldn't open it to find a gritty near-future cyberpunk novel that stops for fifty pages at a time for a Libertarian rant.
You can write whatever you like, but you owe it to the reader to clue them in to what to expect before suckering them into investing their time with you.
It's also a bit like the thing about fantasy magic; if anything can happen, then nothing can surprise. For the fantasy problem, there's no suspense when the writer hasn't promised the heroine can't just rub two feathers together and make the Armies of the Night disintegrate in their tracks. And for fanfic, if you write what looks like a Harry Potter story, and Harry has made it as far as confronting Voldemort, then you don't just have him reveal he was actually a Jedi all along and chop Voldy in two with a lightsabre.
(Well, actually, you can -- but it behooves you to be clear to the reader that this is that kind of story -- and do it before you've made them invest a couple hours reading you.)
And this is tough, because with fix fics and AU stories and cross-overs and re-castings and so on and so forth you've got to put in the work to be clear what the ground rules of your particular fic are going to be.
2. Trim. Especially for cross-over works, there is a temptation to put it all in. There are many stories in the Buffyverse, say, and although you can say the show premise in ten words, the temptation of far too many authors is to set their story late in or after the television series. Which means you've got Angelus and the Initiative and Dark Willow and Ripper and the Potentials and the Buffy-Bot and everything else that was created over seven regular seasons and tons of spinoff.
But go back and look at the actual show. Even late in the run, everything doesn't show up on screen at once. Individual episodes can and usually do maintain a narrower focus.
Me, I think if you are going to muck with the very premises of a property, with or without cross-over, you'd do best to pick an early season/first movie/first or second book. Because there's just too much stuff there, and boy does it all get distracting. That's why my AU Sailor Moon story is set in the Negaverse cycle, and not after you've got Pluto and the Starlights and all the rest mucking things up.
But you can do it with even the more complex properties just by being selective as to what you feel is necessary to include. It's the Checkov's Gun principle; there's going to be a heck of a lot of interesting brick-a-brack in a traditional parlor but you lightly wave over everything but the one thing you describe in detail -- the one thing that will actually come up later in the story. In my SG1 fic, the Asgard are going to play a role in the plot so they get mentioned several times even quite early on. On the Nox, the Tollan, the Furlings, or even the Tok'ra....I have given not a single word.
3. Describe. Two reasons here. First is, you want to be accessible to any reader, not just another die-hard fan. Oh, and even that die-hard fan might not have the same up-to-the-moment familiarity you have if you just archive-binged on the whole thing and are writing with one tab open to the Wiki page.
Second, whether you intend to diverge from canon or not, your take on the characters and situations will be unique (and, really, if it isn't, then why are you writing in the first place?) So you need to describe, describe, describe, because your reader can't be counted to have the same internal image and the same understanding.
And if you've said nothing about your characters, then you aren't doing fiction, You are doing some sort of Mad-Libs with a bunch of names.
And I don't mean hair color. I mean give enough hook into the characters (and places, and conflicts) so the reader can care. Give enough understanding into the characters so the reader feels like they understand their inner workings. This doesn't require a word of narrative description; many plays give everything you really need to know in dialog alone (and so do some classic works of fiction).
And don't just do it once. Especially if someone hasn't been seen for a couple of chapters, catch the reader up. Remind them who this is and why they should care. This even had multiple uses. If you change up from "Buffer Summers" to "The Slayer" every now and then it gives more variety to the narrative, and it gives you a tool you could chose to use to focus in on different aspects of her personality and story.
4. Watch your POV. Even in a visual medium, where it seems like the viewer would be seeing everything and has equal access to the interior lives of everyone, an omniscient point of view is rarely an effective dramatic choice. And fiction is tougher. It is tempting to dive from one head to another, showing the thoughts of every one of your favorite characters and letting the reader know what is happening behind them, in the next room, three hundred years from now on another planet.
But at best, it is distancing. You end up less emotionally involved than if you picked a pair of eyes to filter the experience through. And, harshly, it is rarely done at this level of best. Mostly, it becomes confusing. Pick your POV, clearly indicate your POV through verbal and visual and textual clues, and when you have to shift POV, signal your turns.
(One of the easiest tricks? Name the POV character in the first sentence. Even better, have them viewing or acting or thinking in that first paragraph).
(And, yeah, half the fun of using limited POV is being able to Rashomon events and characters through multiple eyes, through the filter of different perspectives.)
5. Don't be either enthralled by or afraid of "Said." I know, this is really a flaw of bad writing, not a specific to fanfic. But it strikes me it comes out of a style of fanfic that violates at least one rule above; which is to say, uses an omniscient viewpoint and doesn't bother to explain to the outsider. The style of "Jack came up and said, Sue said, the others said, the war was happening outside, all of them said..."
Some writers get afraid of "said" and this is a path that followed too far will lead into Tom Swiftys and worse. It's fine to emphasize a line or two with "shouted," or "whimpered," (and I totally over-use "smiled" myself.) Same for "Said softly" and "Said with a grimace" and so forth. But, really, ninety-nine percent of the time "said" is enough. In certain dialog scenes, even the "said" itself isn't needed, but it is a sort of invisible mortar; it rarely calls attention to itself and thus can be safely left in.
Related to this, there's the great little lesson Mark Twain sneaks in during "Connecticut Yankee"; a story is being told in run-on style, all the dialog mixed together, and the titular yankee stops her and suggests that she give each a distinctive voice. "This Irish knight of yours...have him say 'Begorrah' every now and then."
Well, you need more than that for a good voice. Although when writing fanfic, you can get a certain mileage out of signature phrases and familiar lines. "I'm a Doctor, not a Scriptwriter!" Try to hear the rhythms, the kinds of word choices, that are emblematic of a particular character. It helps greatly to say all your dialog out loud.
And, yeah, these apply just as much for regular fiction. And get violated out there in the real world, even by surprisingly big names.