First I draw each layer I want to animate in Photoshop. Then I import them in AfterEffects, put "pegs" on them, and rotate or move them. I also can add "special effects" to the animation, as well as sound.
This work, here, was an editorial cartoon I submitted to the Winston-Salem Journal. It was rejected, but I liked it so much that I "animated" it in class.
Finally, we had an assignment in class to animate a famous painting. I did A Bar at the Folies-Bergère by Édouard Manet. Follow the link if you want to know more about him.