What a fun class. Melo Pisha, aka Gumdrop, showed us how to make dogs, cats, swords, hats, and some unidentified balloon things in this balloon twisting class. See some of the pictures below.
You can view balloon twisting "how tos" here.
Melo suggests using quality latex balloons, typical size 260 (2"x60") for twisting. Examples here.
In a pinch, Party City will do. And, do not forget a pump... trust me!