Graduation caps aren't cheap, so before you start attaching things to it you should make a plan. Trace the outline of your graduation cap onto a piece of paper to see how much room you have available to work with. Then start thinking of what designs you would like to create. See what colors go well together and make a draft of any words or pictures that you plan to glue on.
Words are an easy way to decorate your cap. Think of names, phrases, or letters that you would like to display. Maybe you want to put the name of a friend or family member who inspired you throughout your education, the name of a friend that passed away or even just your own surname so people can find you. You could attach your school letters to the top of the cap, or alternatively you could write just a short phrase like "Done!" Buy letters from a craft store or cut them out from colored construction paper and glue them to your cap.
Pictures make your cap more visual and allow you to really show off your creativity. Maybe you want to display your favorite sports team, the picture of a friend or family member or even just a shape such as a heart or star. Print the image you want to attach and then use hot glue to secure it in place. Let it dry before adding any other finishing touches.
If you're allowed, consider painting the top of the cap a different color. Use spray paint and cover the entire flat section of the cap in your desired color. You can also attach almost anything you can think of using hot glue. If there is a figurine that you think looks funky or funny, glue that on. Find flowers or ribbons in your school colors and attach those. Or glue on little memento that represents your time at school. So if you were a cheerleader glue on mini pom-poms, mini footballs if you were on the football team or musical notes if you were in the band.