Gauge your audience. Figuring out who you are writing your research paper for can help you determine what kind of funny to work with. If you are writing for your teacher, you can determine what humor is appropriate for her age group, the type of class she is teaching and her conservative or outrageous personality.
Research your chosen topic so that you have both unique or strange facts and meat for your paper. Because this is a research paper, you should have something worthwhile and intuitive to say about your topic. For example, if you're writing about previously banned music or books, your meat would be why items were banned in the U.S., and why they are not banned now. Add insight on how culture has changed so that these items are acceptable now.
Pull readers in with an interesting or questionable hook. This encourages them to continue reading. One example of a hook is: "You might think that Elvis would have been celebrated for his Christmas album, now having sold over nine million copies, but when the album came out in 1957, it was banned from many US radio stations."
Exaggerate wisely with your own voice. For example, add a story from your youth about your parents banning you from listening to something harmless. Exaggerate on what they banned you from listening to add humor and make your point stronger.
Add elements of risque or awkwardness to keep the paper edgy, though this depends strongly on your audience. For example, add in a story about how you tried to listen to the music you were banned from hearing and were caught in an awkward way.
Relate the items you introduced in the introduction to stories you told throughout the paper, linking them to different circumstances so the reader connects the dots.
Contrive words wisely, for example, writing "spied" instead of "saw" and "tumbled" instead of "fell." Create intriguing analogies, for example, writing "still as a scarecrow" or "angry as a bee without a hive."
End your paper with a clever association to the introduction. This ties the entire paper together.