We got a new cat a few months ago. His name is Henry, and the cat adoption people told us they think he's about three years old. Henry seems to think we're mostly okay and allows us to feed and pet him, and we're generally pretty happy with Henry as well.
One relatively minor issue that came up had to do with Henry's claws and where in the house it was acceptable for him to sharpen them. Henry's preferred spot was the rug in our living room, but my wife objected; his second choice was the couch, but we weren't really thrilled with that either.
With some of our other cats we had used a scratching board that we got at a pet store, and it had worked pretty well. It's just pieces of corrugated cardboard glued together in an appealing (to cats) way, and mounted in a little container so that it looks kind of like a small ramp. I had purchased one of these when we first got Henry, and every time he clawed at the rug or couch I or my wife would scold him and move him over to the scratching board to try to get him to use it, but he had expressed indifference, or maybe confusion: "Why should I use this thing when there's a perfectly good rug right here?"
Now that we've had Henry for a few months, we've had a chance to learn what his personality is like. In particular, he's a very methodical cat. He likes his routines, and he likes for us to have routines, and when we deviate from our routines it really irritates him. I noticed that the going to bed and getting out of bed routines seemed to be particularly important, and I eventually noticed that his morning routine went something like this: wake up man (bite his feet if necessary), wait by food dish for man to fill with food (even if there is already food in the dish), eat a few bites of food, go sharpen claws on living room rug.
Since Henry usually went to the same spot on the rug, it finally occurred to me to make sure the scratching board was sitting in that spot in the morning (actually, I put it there right before I went to bed), so it would be ready for his morning wake up, eat, scratch routine.
And it worked! That first morning, he started scratching on the board and I immediately began heaping "Good boy!" praise on him, which he seemed to like much better than the "No!"'s that he'd been getting before. Then when he was finished scratching I went over and petted him for a couple of minutes, while continuing the verbal praise. He pretty quickly figured out that scratching on the board got him a LOT of praise (and petting), and so he started doing it more and more, even waiting until I or my wife or one of the boys was around to make sure he'd get maximum petting.
So chalk another one up for positive reinforcement as a training tool for cats. Next I plan to teach him to mow the lawn.