One way to write a good trivia question is to formulate a question about current events by skimming through newspapers, magazines and media websites for up-to-date information. Make the question hard but not too hard, relevant, fun and customized to the audience you are trying to reach.
To write a good question, think about the trivia players and situation, such as high school students or bar patrons at an establishment near a sporting arena. Consider the category into which the question belongs, and be creative. For example, if the questions are for a karaoke night trivia game, use a musical category such as "Ladies of the Eighties." Research the subject, and ensure that the answer is factual. Depending on the game, rate your question as easy, moderate or hard.
Use a note-taking app, or carry a pocket notebook to take down any interesting ideas for questions you think of during the day. If your favorite movie is on television, find out some interesting facts about the production or the cast, and formulate a question using that information. Another way to become inspired is to listen to the conversation of people who represent the audience for whom you are writing the question. If a particular topic comes up multiple times, find a way to incorporate that topic into an interesting trivia question. Test your questions on someone you trust enough to give you constructive feedback.