To start a Goku crossover fanfic, you need to do some research on both Dragon Ball and the other franchise you're crossing with. If it's a crossover with the Final Fantasy series, understand the magic systems and the different races in that world. Next, create your main conflict. It could be that an evil force from the Final Fantasy world is threatening the Dragon Ball universe and Goku has to team up with the Final Fantasy characters to stop it. Then, just begin writing. Don't worry too much about making it perfect at first; you can always go back and edit later.
First, decide which universe or character you want to crossover with Goku. For example, if it's a crossover with Batman, think about how their different worlds and personalities will interact. Then, come up with a basic plot. Maybe Goku accidentally lands in Gotham City and has to deal with Batman's no - nonsense attitude towards his super - powered antics. After that, start writing an introduction that grabs the reader's attention, like starting with a big action scene between Goku and some of Gotham's villains.