One use of puppets I really enjoy, especially with pre-schoolers, are hand-puppet books. There are lots on the market, but one of my favourites is ‘Playtime Teddy’ by Emma Goldhawk and Jonathan Lambert, which is part of the Snuggle Book series. The key thing about using the book is to treat the puppet as if it's real, then it's much easier for the students to buy into the story. Like all of my puppets, when I'm talking to the class, the puppet looks at me to focus their attention on me. Teddy has a great face, is really cute, and is easy to manipulate too; Teddy can wave, point, clap, shake hands and even tickle. The movements you make with Teddy should be micro-movements to give the impression that the puppet's alive; if you move it too much then it's a distraction. Depending on class size, you can either move around the class with the book, or you can nominate students to come to the front to interact with Teddy. There are a lot more books in this series.
Another book that's lots of fun is ‘Calm down Boris’ by Sam Lloyd. This ties in very well with subjects such as free-time activities/food /hobbies/exercise … Once you've finished the story you can follow up by asking the students their favourite food / what they like to do in their free time, etc. There are 5 books in this series.
Links to the puppet books: