Begin by choosing the other universe for the crossover carefully. Consider which elements of that universe will contrast or complement the 'Journey' world. Then, focus on the emotions of the 'Journey' character as they enter this new world. Are they scared, excited, or curious? Build the story around their exploration of the new place. You can also introduce new characters from the other universe who will interact with the 'Journey' character and drive the plot forward. For instance, if it's a crossover with a historical - fiction world, how will the 'Journey' character deal with the different social norms?
First, know the two universes well. For the 'Journey' part, understand the themes of connection, exploration, and the unique visual elements. Then, pick a starting point. It could be that the 'Journey' character wakes up in the other universe. Next, introduce the conflict. Maybe the 'Journey' character's way of communication doesn't work in the new world. Start writing simple interactions to build the story.