Go to the dollar store. Find the party section. Your main priority is kazoos. Get all of them. This is the most important step in the entire process. You can get other party supplies too if you want. For example, you can get special hats for the graduates, and regular (cone-shaped) party hats for everyone else.
Find a place to do the ceremony. You could use the corner of your local park, or a gazebo, or a parking lot, or the outdoor section of Big Box Store. Try to think of a place that you can use for free without getting kicked out. The location will ideally have some kind of naturally occurring stage that the graduates can walk across and shake your (and any other officiants') hand while collecting their diploma. Speaking of that...
Make some diplomas. See the picture for inspiration.
Invite some people, including the people that are going to get graduated, obviously. You don't need to ask them if they are good at playing the kazoo, but you can if you want.
Write down some quotes that you can say during the ceremony. They don't need to be based in reality.
Okay, now you and everyone are at the actual ceremony. You're on the stage, and playing some kind of welcoming song on your kazoo as everyone approaches.* Everyone except you (probably including you) are clueless about where to go and what to do, so you'll have to wave your hands around a lot. This is okay and in fact adds to the aesthetic of the event. Try to get all of the graduates to stand on one side, and all of the observers to stand on the other side, forming an aisle in the middle. Everyone is facing you.
*In our case, since the event was held on Christmas Eve and was held under this giant tree, the only thing I could think to play was Oh Christmas Tree. Your selection will likely be superior to mine.
Stop playing your kazoo and silence the crowd in any way you see fit. Welcome and thank the audience. Say some things that sound like things that would be said at a graduation ceremony. This is where your preparation from earlier will come in handy.
After you're done talking, command everyone to get their kazoo out and to join you in playing Pomp and Circumstance. Now the graduates will walk across the stage, shaking the hand of you and all officiants as they collect their diplomas. Feel free to add some kind of physical ritual here. For example, you can snap their hat, spin them in a circle manually, etc.
Once all of the graduates have had their hands shaken and have received their papers, it's very important for there to be a clean finish to Pomp and Circumstance. Act like a lunatic conductor and cut off the final note with a huge wave of your hands and/or body.
If you feel compelled to do so, you can say some more things to the crowd. Then, there needs to be a moment of transition in which everybody knows that oh man, this just happened. So count to three, and on three, have the graduates throw their hats into the air. Or do something else—use your imagination.
Now everybody is graduated and you're on the cusp of being arrested for a noise violation. So get out of there.