To start a Super Smash Bros crossover fanfic, begin by choosing the crossover elements carefully. If you're thinking of a crossover with a superhero universe, like the Marvel universe, consider how the powers of superheroes will mesh with the Smash Bros gameplay. After that, outline your story. You might want to start with a conflict that brings the different characters together. For instance, a powerful villain from the crossover universe threatens the Smash Bros world. Then, write the first few paragraphs introducing the situation and the main characters involved.
First, decide which two or more universes you want to crossover. For example, if you choose Super Smash Bros and Mario Kart, think about how the characters and elements from both will interact. Then, come up with a basic plot. It could be a tournament where characters from both universes compete. Next, create some unique scenarios. Maybe the Mario Kart tracks are now part of the Smash Bros battle arenas. Start writing simple descriptions of the characters and their reactions to this new crossover world.