Question
Can you root trees from the limbs that are being pruned off of the tree? If so, what would you need to do?

Answer
You can try but I think what you will get is not the same "bradford tree" since normally bradfords are a combination of a Shapely pear grafted onto a thorny root stock. But what the heck if you have time try it--check with a garden/ nursery type store and get a rooting hormone and keep the cut stems wet and not too hot. Cut about 6-8 inch ends of a branch and put into damp sand after the rooting hormone  insure the stems that are green and flexible for the rooting stock. You should see roots in about 2-3 weeks and when the root system is developed you can transplant into a pot with a good potting soil.