I want to change the texture of specific objects, making shift across the surface of the object. I don't know how to insert keyframes for UV mapping though. How can I make the image on the object move? Think of a magical cape, with the design constantly flowing on the cloth. How could I achieve something like that?
Add a new material to your surface and unwrap it. Give it two image textures (set their type to Image or Movie and mapping coordinates to UV). Now add one more texture. Set its type to Blend and place it between previously added ones. In Influence panel uncheck the Color box and check Alpha. Check the RGB to Intensity and Stencil boxes.
In Mapping panel change the Offset value of the X window so you can see only one texture. Hovering your cursor over that window press I to insert a keyframe. Go to another frame, change the Offset value and press I again.