You can start by creating a character profile for the characters from both shows involved in the crossover. For Special Agent Oso, list his skills, his catchphrases, and his personality traits. Do the same for the characters from the other show. Then, find a common goal or problem that they can all work towards solving. This could be something like saving a group of lost animals that are important to both worlds.
First, decide which other show or story you want to crossover with. Then, think about how the two worlds can meet. For example, if it's a crossover with a space - themed show, maybe Oso gets sent on a mission to outer space by mistake. This gives you a starting point for the story.
Begin with a scene that sets the tone for the crossover. If it's a crossover with a spooky - themed show, start with Oso arriving at a haunted house as part of his mission. He quickly realizes that this place is different from his usual missions. Describe his initial reactions and how he tries to adapt. This will draw the reader in and introduce the crossover element right away. Also, don't forget to establish the rules of this new combined world early on in the story.