First, re - read the Twilight books to really get a feel for the world, its rules, and the characters. Then, come up with an interesting concept. It could be as simple as a 'what if' scenario, like what if Bella had a different power. Next, start creating your own characters or expanding on existing minor ones.
Begin by choosing a specific aspect of the Twilight system that you want to focus on. For example, you could center your fanfiction around the werewolf pack dynamics. Then, think about the conflict in your story. It could be an internal struggle within a character or an external threat to the Forks community. As you write, don't be afraid to deviate from the original a bit to make your story unique, but also stay true to the essence of the Twilight world.
To start writing Twilight system fanfiction, you need to have a clear idea of the tone you want to set. Are you going for a more romantic, action - packed, or mystery - based story? After that, do some research on vampire and werewolf lore in general. This can give you more ideas to incorporate into your fanfiction. Also, make an outline of your story so you have a roadmap to follow as you write.