Answer:
You get you some leather (glove) oil and rub it in, following the directions of course - don't overdo it at first. Put a baseball in the mitt part where you want the ball to be caught and tie a rubber band around it to keep it very very tight. Place it under your kid's mattress for a couple of nights so they sleep on top of it to break it in some more. Then you just undo the rubber band, take the ball out, and throw it hard into the ground a ton of times, preferably grass or carpet and not dirt, and stomp on it with your shoes and stuff. Fold it in and out every which way possible, roll the bends back and forth really hard. You can even run over it with the car a few times (without the baseball in it!). Then re-oil it and play catch for a couple of weeks to break it in, which will probably be done in baseball practice anyway.