Puppets are so fabulous for storytelling. Puppet shows can be ad-libbed or planned, written, and performed. Mo Willems's Elephant and Piggie books make great "scripts" because they are straight dialogue.
You can use purchased puppets, or make your own! The possibilities are endless: sock puppets, stick puppets, bag puppets, marionettes (ok, maybe that's a bit much...)
Although we do have a fancy schmancy puppet stage at TRWR, all you really need is to cover a table with a blanket (or just go behind a couch) and stick you arms up!
Puppet shows are the kind of thing that sometimes happen spontaneously, and sometimes happen in a more sustained way over a few days. A story idea (or improvisation), time, materials, and an audience are all that are needed.