Everyone's process is different, but there are certain components that are nessassary: brainstorm, write, revise, revise some more, conference and listen to what other people think, revise some more. One step I personally add is "talk to yourself and play out a scene in the privacy of your own home, thus creating odd stares from your dog."
Revision is a HUGE part of writing. Many young writers (and by young, I mean in experience, not age) will start sharing their personal writings. That is great! But you need to get to the stage where you are comfortable actually asking for feedback. When that feedback happens, really use it! And I don't mean, post your poem on Yahoo!Answers. Take it to a teacher or writing group and really imporve on your capabilites. Revision has the word "vision" in it for a reason, you need to see your work through another person's eyes.
Being original, coming up with your own unique plot, and developing your own voice is just much better exercise than fan fiction. If you want to improve as a writer, you have to handle the creativity part, and you aren't as creative when you are using other people's ideas.
Did I ever imagine new possibilites for things I read or saw? YES! Did I write fanfiction? No! It is a fruitless endevour for me. You can't publish fanfiction (there are laws against using someone elses ideas) and you are mimicing an author's voice instead of honing your own. If I was going to put the time and effort into writing something, I wanted it to be a Sara Barton original.
I've got a couple book ideas in my head. I started thinking about Katrina and the crew years ago. What I would like for my second book, isn't feasible right now (See, there's this war going on in Iraq, and I would sort of need there not to be a war for the book to work.)
There's also a bevy of secrets the reader doesn't know. I'm not telling what they are here, but I can't wait to write more books and share them that way.