I think it's easier to train cats to do things, than it is to not do things. ie you can teach a cat to come when called, or a bell is rung, or light flashed etc, so long as you feed it when it comes. It'll rapidly associate the two, good old Pavlov at work.
It's harder to stop the little buggers from doing something, like scratching their claws on the furniture, or digging up your freshly laid lawn.
Rather than training them, it's generally easier to either provide a better alternative, or some mechanism to make what they are doing less comfortable or acceptable to them. Eg, one mechanism to stop them digging at the furniture is to wrap the item of furniture with baking foil, apparently they dislike the feel of this on their claws. Another approach is to provide a proper scratching post (or similar), since this is normally much more acceptable and works better, since they scratch to remove the dead outer layer of their claws, it's not purely destructive!
