It's kind of like asking "how is a motor vehicle made?". It just begs a million more questions. A vehicle for use on snow? On water? On streets? Off-road? For how many passengers? One? Four? Three-hundred?
The one common ingredient in building muppets is creativity. There is a need for a specific puppet character or character-type and then the creative puppet builders use whatever materials they have/can find to bring the idea to life! The skills of each individual builder will dictate the approach to some degree. A builder who is very skilled in sculpture might be more inclined to carve a foam head whereas someone who has a lot of experience in pattern-making might be more inclined to designing a character to be created with sheet foam.... assuming that the design and character even dictate a foam head!
There is simply NO simple answer to this question. Necessity is the mother of invention, and every puppet is an invention in its own right!