With my small Kubota, I bring the loader bucket up about 4 ft off the ground, put the tractor in low, roll up and stop with the bucket just touching the tree, hit the differential lock, and press the hydro pedal all the way down. Usually it will push over a tree about six inch diameter at the base, but not a six inch Florida Pine. Once the roots have pulled up a little on the side where the tractor is, I dig down a few inches with the bucket, used the same procedure to push forward, but curl the bucket up after it goes under the roots. Repeat these two steps a few times and most small trees come right out. With a tree that has a real deep root ball, I've been digging around with the backhoe a little before I push it over.
I don't know if there's a right way or not. Just go with trial and error, without beating up the tractor. In other words, no full speed ramming action and you should be OK.