Wet your paper. Wad it up in a ball . . . maybe multiple times.
Flatten it out by hand; then iron it if you want it smoother. Fun and easy!
On my elephant you may notice that I cut an additional head and layered it on top either with foam tape . . . or in this case I folded a piece of paper making a paper hinge. Attaching this underneath gives the head some dimension and movement. I also used mini-brads for the eyes.