I started out writing fanfiction in 2006 and very quickly thereafter I began to write original short stories and eventually in 2009 began writing novels.
It is difficult coming up with original ideas, but there are some tips that I've picked up along the way, either by reading articles, taking enrichment classes, or just talking to readers. Here is what I would suggest:
1) If you're like me, then you have a certain genre to which you are drawn. When you initially write original fiction, stick with that which you know. For me it's zombies or some other kind of horror. This keeps you feeling comfortable while you venture into the world of original writing. When you begin to feel comfortable (for me I started feeling less and less like writing fan fiction because it felt less rewarding than writing something of my own), then you can start to explore new subgenres, like say, vampires rather than zombies, etc.
2) You can pull ideas from the world today, and many established writers do this. I do not, incidentally
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3) Ideas can also be looked at, not so much as 'This is what my story is about (plot)". You can do this, that's how I wrote my first zombie novel. However, it is not how I wrote most of my short stories. Most of my initial seeds for writing a story have more to do with a certain tone or emotion I want to convey in the story (this is good for short stories because you must pack a lot of emotion into very little writing, so I find that it makes most sense to write the story to establish strong emotion, fears, hatred, love, etc). Usually it is loss or longing- everyone knows these feelings very well and so they tend to be easy to write. Note: If you feel sad, remourseful or shocked during your story, so will your reader.
4) Another way to get your initial seed is by way of a specific character you want to write. These are good for all kinds of stories, but I find they are best for adventure and also emotionally driven stories. When you have your character you are driven to write, it should then be easy to develop an appropriate setting for a character, especially if following suggestion number 1, in which you go with which ever genre you are most comfortable.
5) Make a list of ideas; keep a notebook or piece of paper handy. Jot down and interesting looking stranger you saw on the way to work perhaps, or something you would like to see happen. Maybe an intriguing question you have, or a strong emotion you are feeling. Eventually you will be able to spill ideas onto paper without even thinking about it. After you have a list, set it aside for a week or so and then go back and see what still sounds good. This will generally be a good starting point.
Once you have a little piece of the puzzle, if should be relatively easy to build upon. If you'd like more tips on writing in general, I'd be more than happy to help.