Full disclosure: I found the instructions for this puppet project on-line. (I didn't want to have to fall back on my paper bag puppet just yet.) I'd goofed around with stuff like this before, but I actually thought I should follow directions for once. I also really wanted to post up something fun for kids to make.
And you can be a lot more creative than my mock-up!
It has a pretty nice rebound spring!
This is best suited for ages 8 and up. Some of the folds are tricky -- especially towards the end. There are a number of sites that have this particular project, but this was the one with the best, stey-by-step instructions. The paper folds create a "hinge" that actually some push back to it (like using a compression spring to keep the mouth open).