To build a puppet, I first have to get the character in my head down onto the paper. Sometimes this comes easily, other times there's kicking and screaming. Draw, draw, draw. Lots of paper might end up in the recycle bin, but better than fur and feathers.
I like to use Prismacolor markers and a Sharpie pen on plain printer paper. Once I get a black and white sketch that I am happy with, I scan it, then print it out. That way, if I mess up in the coloring process- I just print out another page and color again.