Strangely enough, you asked the question that most people try to avoid asking. When most people ask "how do you make a puppet?", they're really asking, "How do you build a Muppet?"... meaning they want the kind of visual results one sees when looking at Henson characters. They can identify that there's specifics involved, but they don't know what to ask. But in asking how to make a puppet, they're phrasing the question so generally that they'll invariably get the answer, "Be creative" or "Experiment".
When one asks, "How do you make a puppet?" one might as well be asking "How do you draw a picture?" There are a million ways to draw a picture. Maybe more. Starting with more drawing substrates than I can name, millions of drawing tools (including computers!), choice of subject matter, and artistic style. But if you get specific and ask, "How do I draw a picture that looks like a 1950's animation drawing of Mickey Mouse?" you will probably be able to find the specifics of how that is done. For starters, you won't use a felt-tip pen. You'll use a pencil. Perhaps several colors of pencil. And you'll do it on smooth, white paper... not something like watercolor paper or construction paper or bristol board. Etc. In the end, you'll probably learn a lot about the process of animation drawing that you'll be able to apply to other drawing projects. And that will make you a more proficient artist. The same applies to puppet building.
Most puppet builders know there are no hard and fast rules for making a puppet... only knowledge of materials, good techniques, efficient tools, and personal skills. How you combine these things allows you to build a puppet. And if you combine them in a certain way, you get a puppet that looks "Muppet-y".
The best resource I know for beginners is not a book at all, but the patterns available through Project Puppet. I often come off sounding like a paid spokesman at times, but I cannot say enough good things about their stuff. I own many of their patterns and have found them to be useful in the extreme.
Not only do they provide you with a VERY usable pattern, but they give you practical instruction on materials, techniques and methods for building Muppet-y styled puppets in general. Once you know these things, designing your own Muppet-y type puppet becomes much easier. But its a cumulative knowledge that lets you do that. And you have to start somewhere.
Which is why I always recommend the Project Puppet stuff. Its a tremendously informative launching board and educational tool.
-Gordon