First, re - watch the show to really understand the characters, their personalities, and the overall tone. Then, come up with an interesting concept. It could be something as simple as a day in the life of a minor character that we didn't see much of in the show.
You need to be familiar with the rules of the Dead Like Me world. How do reapers operate? What are the limitations? Once you have that down, start creating your plot. Maybe it's a love story between two reapers, but you have to make sure it fits within the framework of the show. For example, how would they handle their jobs while being in a relationship? Also, don't be afraid to add your own unique twists to the story, like a new type of soul - collecting device or a different afterlife bureaucracy.
When it comes to writing, make your characters believable. Even though they are reapers, they should still have emotions and motives that readers can relate to. Use vivid descriptions to bring the world of Dead Like Me to life in your fanfiction. Describe the drab offices where the reapers get their assignments, or the unique look of the souls they are collecting. And always proofread your work to make sure there are no grammar or spelling mistakes.