Cool! I love to write stories and also give advice so this should be fun. (I've only finished writing one of 3 stories, which was pretty short. The first one I began I quit because I got a big writer's block and lost interest. There's one I'm doing right now that I hope to publish if possible. I may continue the first story sometime and try to publish that too.)
1. Think things all the way through before you run into a terrible writer's block that forces you to make annoying changes.
2. Be careful how you set things up so you can make things more mysterious if that's a goal.
3. Don't be too serious but don't be too funny either. Have more range of emotions if you want a really great story (but The Blue Toad's "The Mushroom Ball" was very funny and still a great story)
4. Decide what your story will be like to decide how you'll write it. If you want it to be somewhat accurate to the games, try to make the story feel like the game by having some certain elements of the games. If you have a romance story, scary story, etc, then prepare your writing style to acheive that.
5. Prepare to be disappointed because there's a chance that few if any people will read the whole story or any of it (especially the really long ones). I started to read a great story from Jman, I think, about Tatanga attacking the Marios and Warios to steal their blood, but I stopped reading it because it was so long. (And I'm too busy now anyway, sorry.) But remember that there are other websites you could give it to.
6. Try not to offend people with things that you think might be a little too much for some people (and that could get you booted).
7. Keep practicing your descriptions of scenery, feelings, thoughts, words, etc. to really make a good story.
8. Read lots of other stories from good authors. Pay attention to plot elements and how the author does things.
9. Don't write something like The Prophecy where you don't finish it for an eternity. I almost guarantee you WILL regret it for a long time!
10. Help Yoshisaurus Rex out by answering his question in "Publishing Perplexion: Need help!" He will then give you a Yoshi cookie.