I started out planning to write an article about how to write fiction but in doing research I found that others have already done that so much better than I could. So what I have done is compile a list of links to ideas that you might find helpful in your writing.
To be brutally honest, I find a lot of errors in fanfic that frustrate me and make me shake my fist at the education system today. Please, I beg of you, take the time to go through all of this, especially the first two articles. The grammar book link is a good overall reference but please also at least browse over it.
Now I have to go and apply these principles to my own work because I have forgotten enough of this that I am embarrassed to admit to being an English teacher. Please do as I say, not as I do.
Read this first: http://www.guardian.co.uk/books/2010/fe
The above is an article in which well known authors list rules for writing fiction. I include this not so much for its helpfulness but for the joy of reading it and the amusement it will provide. Notice how remarkably similar some of the advice is.
The information found at http://www.waynesthisandthat.com/writef
Everyone needs a refresher on grammar, spelling and punctuation. A good guidebook can be found at http://www.grammarbook.com/english_rule