First, decide which two universes you want to cross. For example, if it's Kakashi and the DC universe. Then, think about how Kakashi would fit into that world. What would his first encounter be like? Maybe he arrives in Gotham City. Then, start creating a plot. It could be that he has to team up with Batman to stop a common enemy.
Begin by outlining the characters. In a Kakashi and Star Wars crossover, you need to consider how Kakashi's ninja abilities translate in the Star Wars universe. Is his Sharingan like a new form of the Force? Plan the setting carefully. If it's on a Star Wars planet, how does Kakashi adapt? Start with a strong opening scene, like Kakashi crash - landing on a strange planet filled with Jedi and Sith.
To start a Kakashi crossover fanfiction, you should focus on his character traits. Let's say it's a crossover with the Lord of the Rings. Kakashi is a skilled and intelligent warrior. How would he interact with the hobbits or the elves? Create a conflict that involves both universes. Maybe an evil force from Naruto's world is trying to take over Middle - earth, and Kakashi is sent to stop it. Then build the story around that central conflict.