How do you make a puppet?

Today we went to see the puppet exhibit at the museum of anthropology. This was actually why we came here right now—I saw the exhibit for 15 minutes on a work break and resolved to come back to spending more time with the show. The puppets from all around the world and spanning hundreds of years are amazing. I sort of want to give up all my other projects and just make puppets. I could make their hands and faces or air dry clay and make clothes for them on the loom!