I need to build a model of the Happiness Machine for a class project. Any suggestions on how to do it and why?

That sounds kind of challenging to me, but I'm the one who always fell flat on his face in art/home ed/shop kinds of things. I once made this diorama that looked like a post-apocolypitic wasteland (I think it was supposed to be a happy zoo), and a stuffed squirrel that looked like an escapee from the Island of Dr. Moreau.
Debby, I wish you good luck.
If I were in your shoes, though-
The book describes the actual machine as an "eight-foot-high orange colored box". I assume you will be working in miniature. Eventually, however, the Happiness Machine that Leo builds in his garage is a failure and burns down. The real Happiness Machine, that he sees at the end of the chapter, is his own imperfect but wonderful family and imperfect but wonderful life. If that's the happiness machine you want to portray in your project, that would be another option.
You've got a tough job, Debby. The problem is that you have to build a model of an idea- that somehow, the Happiness Machine by its nature defeated itself. It's kind of abstract, so again good luck. Maybe you could do more work with the stuff that Leo put into the machine- vacations, sunsets, and all that stuff, and then somehow show that the fact that you can't and shouldn't stay in the machine forever is its real fault.
I hope this helps stimulate your creativity. Your project is hard to do well, but certainly not impossible.
Best of all possible luck,
Dan