How to move the character… in basic like walking, running
Such a broad question, so I'll give you a broad answer.
For a game using jME-Physics, you'll want to add forces to the objects to make them move.
For a game not using jME-Physics, you'll want to update the local translation during the update() method. There are InputHandlers for things like that (FirstPersonHandler, NodeHandler, ChaseCamera & ThirdPersonController, etc), which will assist you greatly.
Usually the InputHandlers manage stuff like this for you, but if not you'll need to bind keys to actions, for which you'll like to see the KeyBindingManager class, and all of it's methods. Keep in mind, it's a static reference, not an instanciable class.