So here goes, my collection of rants, guidelines, and so on.
Use a spell checker. If you're not good at grammar, get someone who is to proofread, and learn about it yourself. Learn the rules of punctuation, and how to write dialogue. It's trickier than you probably think. Get your tenses right; if it's past tense (the most common) stay in the past, if present tense, stay in the present. Paragraphing is important; each paragraph should contain one general subject or thought, start a new one when you change thoughts. Also, you must start a new paragraph whenever you change speakers.
Proofread several times. If the piece is longer than a few pages, wait a few days and proofread a few more times. Ideally, for something long, put it aside for at least a week, then go over it again with a fresh eye.
In summary, try to make it as perfect as possible. Everyone makes mistakes. But don't put a piece of crap out there out of laziness and/or sloppiness.
On the other hand, many other writers are too brief, with a story that moves way too fast, with no atmosphere, no description of setting or emotion or appearance, often without bothering to mention where the action is taking place. There's a happy medium.
In general, every sentence, every word, should serve a purpose. It may advance the plot, develop a character, set a scene. If it's there to be amusing, be damn sure it really is amusing. Don't repeat things endlessly. We only need to see one or two scenes with the characters expressing their deepest feelings, not twenty. Don't have repeated scenes of characters discussing unimportant things, apparently just to pad out the story. It gets boring, very fast. At the same time, take the time to slow down and explore what the characters are feeling once in a while, and what they're seeing, hearing, and doing, as long as it says something relevant and new about the character or the situation. What you write should be enough to make the reader 'see' what's happening in the story, not enough to slow things down.
I can't give much advice on how to construct a plot. It takes experience and hard work -- and probably talent -- to collect ideas and put them together into a story that makes sense. Ideas can come from anywhere, other stories, movies, TV, your fantasies, idle conversation. You need more than one idea for a story of any length, ideally a plot thread/subplot for each major character. Try to weave them together, relate them to your central theme. This will make for a multi-dimensional, more interesting plot. And beware glaring plotholes. It's vital that the story make sense; artistic license is one thing, laughable mistakes, forgotten events or characters, resolutions that come out of nowhere, actions that are jarringly out of character, are all something else and will turn off many readers instantly. Take the time to do it right.
Again again again, take your time. If writing something of any length, don't type it out, proofread once, and post it immediately (probably at 2 AM). A day or two may have you rereading it and wondering what the heck you were thinking. Post in haste, repent at leisure.
This gets me into a semi-rant; I honestly don't understand why so many fanfic writers write and post one chapter at a time. This works well for an episodic story, in which chapters pretty much stand alone; maybe not so well for stories with an overall plot, especially if it's fairly plot-driven. It seems very limiting to me; there's no way to go back and make changes later on if you want to do something differently or spot a mistake or inconsistency. I know it's the usual method, and some writers have the discipline to stick to detailed plot outlines and do it effectively, but it just seems to me to be a recipe for plotholes, inconsistency, and bad pacing. Believe me, the main reason my stories are tightly plotted is because I finish them before starting to post.
Plot involves characters, of course. A good plot will result in the main character(s) going through some kind of growth or learning experience. This is good character development. You can show the character change (to a reasonable degree), or you can show him/her fail to change.
Again, your story should make sense for your characters. Don't force them into situations just because you think it'll be neat. Don't have a previously decent, moral person suddenly beating his girlfriend or killing someone without a compelling reason, that's not neat at all and will only upset readers who like that character. Take the time to think it out, make it happen naturally. Every event should have causes and effects. Equally, the characters should do things that are in character, realistic, and reasonably logical. They will not always do the sensible thing, that's human nature. But what they do should make sense, for that character, at that time.
This doesn't mean you can't do out-of-character stuff. One way is to write an AU (Alternate Universe). Remake the characters any way you want, as long as you warn the reader and give them some idea of the new rules you're playing by. (However, if you're going to make them into different characters, you might as well just give them different names. It seems pointless to me to write fanfic that's not about the characters we know.) However, you don't need to go the AU route, you can make a character do almost anything you want, IF you build up to it, make the reader believe it, put him/her into a situation and through an experience that makes normally out-of-character actions seem real.
Don't use the idiot plot. (This is from Siskel and Ebert.) The idiot plot is a story which only works because every character in it is an idiot. For example, most slasher movies -- there's a mad killer out there, so the teenagers all immediately wander off by themselves to get killed.
Make your main characters real. Even the most wonderful hero has flaws and weaknesses. Even the most despicable villian may have a good quality or two. Complex characters are much more interesting than cardboard ones.
Yes, characters can change -- that's part of writing a good story, showing the main characters growing and learning -- or failing to learn. But people don't change overnight, and they don't change completely. A character who starts out mean, violent, and unfriendly is not going to have one uplifting experience and suddenly become a heck of a nice guy. (Unless his name is Scrooge.)
Some fanfic writers like to create original characters, some don't. Both choices are valid, in my opinion. However, there are some pitfalls involved in original characters (OC's). The main one is the common delusion that readers will become as fascinated by them as the writer. Fanfic readers want to read about their favorite canon characters. Period, for the most part. With very few exceptions, it's much wiser to keep your OC's in the background.
That said, I think it's a good idea for a writer to create new characters. It's a challenge, it's fun, and it gets you out of the limitations of a fixed set of canon characters. The most obvious use for them is as villians. They can also be supporting characters. They should be important to the plot, but not take over. As long as you keep in mind that the canon characters are the stars, you should do okay.
The other definition of Mary Sue is the author's projection of herself into the story, a sort of standin. I personally don't think this is necessarily a bad thing, if done right, but that's a very big 'if'. Speaking from my experience, I made one of my OC's similar to myself in several ways, and quickly found that she was the most difficult character to write, largely because I had to watch out for making her too nice, too funny, etc.
And don't think you're safe from Mary Sue just because you're writing only canon characters. I've seen it many times in Power Rangers fics, and I'm sure it happens in other fandoms. The female Rangers, especially the author's favorite, are incredibly beautiful, understanding, sensitive, wise, always right, much smarter than the men, and most of all (God help us), kick-ass feisty. This may be fun for many fans of the show, but it's not good writing.
We've all heard of first-person, third-person, etc., I won't explain what they are, just the pros and cons of each.
First person: This is the most personal of the POV's. Since the primary character is 'talking' directly to the reader, you may get all of his/her thoughts and emotions, along with a strong flavor of that character's personality and speech patterns. You can do some interesting things with this POV, the narrator can tell all honestly, or he/she may hide or distort things, perhaps without realizing it. It's the most intense way to identify with a character. On the other hand, with first person you usually (but not always) stay with the one POV throughout the story, meaning you're limited to what that one character experiences.
Third person is much more commonly used, and what most of us are used to reading. There are several varieties:
Outside Observer: Views the action from the outside. None of the characters share their thoughts or feelings. This can be very useful, but should be used sparingly, since it makes for pretty dry and unemotional storytelling.
Omnicient third person: Tells the thoughts and feelings of all the characters, jumping from head to head. While this is the most popular method in fanfic, it's not my favorite, and takes a certain amount of skill to do without disorienting the reader by tossing him/her from character to character. If you're going to use it, limit yourself to one character's head per paragraph. I've seen this POV used to good effect by experienced and talented writers, but my personal opinion is that it detracts from the story in almost all cases, diluting the intensity with which a reader will identify with any given character, confusing if not done right, and destroying a good amount of suspense since you know exactly what every character is thinking. You almost never see it in professionally published fiction, and there's a reason for that.
Limited third person: This is what I recommend, as you might guess. Get inside the head of one character at a time. It's up to you how much of his/her heart you want to reveal. You can change POV's, but use a scene change, marked with a separator -- a blank line, a line of asterisks, whatever -- this warns the reader to shift mental gears. Pick a few main characters and use them as POV characters. How many is up to you, for a short story I'd say not more than two or three, for a fairly long story not more than four or five. Of course this is just a general guideline. Avoid using minor characters as POV's, this can be effective if done properly, but it may lead the reader to think they're more important than they are.
Well used POV will strengthen a story. In scenes with more than one possible POV character, a lot depends on which one you choose to use. There will be situations when you want to show what a particular character is thinking, other times when it's more effective not to show it, or to show it by implication. It's surprisingly effective to show emotion from the outside, by describing facial expressions, tone of voice, and actions.
Maybe most of all, pick a POV and stick with it. Remember, if you're doing first person or limited third person, we're not going to know what any other character is thinking unless your POV character is telepathic.
'I suck at summaries.' PLEASE, please, for God's sake don't say this. I have seen it hundreds if not thousands of times, and it's irritating just from that alone. It's not just me, I've seen the same complaint dozens of times from other fanfic readers, along with the statement that they never read a story with a summary saying this. Saying anything like this gives a terrible impression. Try harder. It's not all that difficult to write a summary.
Author's notes - don't put them inside the text of the story. It brings the reader right out of the mood. Anything you want to say can be put at the beginning or end. Similarly, put a divider of some kind between author's notes and the actual story, we'd like to know where one leaves off and the other begins.
'I'm posting this at 2 AM and it probably doesn't make sense.' Probably not. Get some sleep and fix it.
'I can't remember the name of this character/device/place.' Look it up.
'I can't be bothered to write this scene, but they all do so-and-so.' Actually saw this stuck in the middle of a fic, thought it was so outrageous I just had to put it here. A variation is writing such a brief and incomplete scene that you might as well have left it out. If a scene's necessary, take the time to write it well. If it isn't, just skip it and have the characters remember it/talk about it/whatever.
'START FLASHBACK' 'END FLASHBACK' Yeah, I know, maybe this is just your style. It really doesn't look good, and again brings the reader out of the flow of the story. The narrative should move smoothly in and out of flashbacks, without needing an announcement. A line or two stating the character is remembering something, a couple of "He had been out walking his dog when it happened" type sentences, and then just tell it.