I have not done fan-fic per-se.. but I have written for and been involved with fanzines.
The best advice is to write, Write, and write some more.
Don't worry about style, grammar, or what the audience might think.. just get it out on paper.
Then comes the fun part.. re-write.. edit, make changes.. check your facts.. and then re-write again...
By the time you have re-written it four or five times you are probably close to where you want it to be.
Let some one else read it. Not someone who will spare your feelings.. but someone that cares that it's good, and who knows the genre and audience.. take their advice, but only as advice.. re-read their comments against your work.. if it makes sense then make changes, if not.. still think about making changes..
Next probably comes another re-write, and then maybe a few more for good measure.. Finally, send it off to a zine publisher or put it out for eyeballs to enjoy.. and wait for the slams.. they will come.. For every good comment will be six or seven who will consider it bird cage liner.. ignore them.. But do look for good solid criticism.. and then.. SEQUIL~!!!!! "muahhhhahhhahhaaaaa!!!!!!!"
And then you is a writer my son..
Have a ball and write, write, write..

Oh, yea.. and maybe look in on a few writing how too books, and books that tell you how to write.. those poor schmucks need the money..

(A final note on publishers? Guess what... more re-writes and editing.. but from them it is usually only to make the work better, more readable or fit the issue. They are good sources of advice.. but remember.. your story is your own - not theirs.. Shana)