Cats climb by using their claws on all four of their paws. They pull themselves upwards by digging their claws into the surface. Because cats require claws to climb things, declawed cats are not very good climbers. Most (if not all) cats should be kept indoors, especially declawed cats. Declawed cats cannot easily climb things (such as trees) in order to get away from predators.
Below are some impressive pictures of Mocha, one of our friend cats, who climbs the screen door. Mocha is an indoor cat. Do you think she is climbing the screen door because she wants outside, or is Mocha just having a good time?