What you want to do is us a double boiler and melt down your clay until it is a liquid. From there you can dip your armature into it to coat the entire thing. You can do this several times until the clay is thick. That's the best way to do it. There are tutorials in the store if you want to see examples. Particularly the puppet sculpting tutorial here:
I also have a free playlist in the tutorial section of this page of me creating a blue monster puppet. I go over most of the techniques there:
Either of those should get you on the right track. If you do end up making your puppet make sure to share a picture or two. I'd love to see how it turns out.