My fan script was my first screenplay. When you're starting out, it's easier to write about characters that already exist, so characterisation isn't too difficult and you can concentrate more fully on other things like plot.
It's supposed to help if you plan each scene and write a little summary to work from. Personally I didn't do this, because I absolutely hate working from a plan and it never helps me anyway, but it may help you, I don't know.
I just use a pad of paper to scribble on. Write down a basic plot outline, scribble ideas as they come to me, lines of dialogue I think sound good, that kind of thing, and tick them off when I get them down in the body of the story.
Maybe some of that will be of some use to you. Good luck.