The Max costume is a simple jumpsuit with big fake buttons and a tail made from fake fur, along with a fleece crown. The Wild Thing outfit is a long sleeved shirt and pants made from flannel. The scales on the pants were drawn on with a Sharpie. Everything was made using homemade patterns.
The most difficult part was the headpiece for the Wild Thing. For details on the construction of the Wild Thing's headpiece, please see my instructable "Wild Thing Headpiece."