I think I agree with all the previous replies and especially with what CheeFatt has said. I would also like to add a little.
I think I recall Yang Chengfu being quoted in Da Wen (?) (Questions and Answers?) with an answer to a similar question as the one originally posted here. If memory serves, he said that no matter how fast and furiously the opponent throws punches and kicks, he or she must attempt to touch you to do real harm. With that attempt, you can make contact and begin to “follow.” If you follow correctly, you will overcome.
Push hands is training and not sparring or fighting; however, push hands ranges from the very safe and highly stylized to the somewhat dangerous and highly variable. Even beginning applications of many of the eight energies can cause serious harm. They are not merely artificial exercises with no martial purpose.
One point of push hands is to understand the use of energy. If you understand enough, you can apply long energy to move your opponent safely, but powerfully, across a room. You can also apply short energy in the same configuration to allow the same power to remain in the opponent’s body with no movement across the room.
From what I have read and been told about combat theory, Taijiquan teaches that you want to make physical contact where possible in order to allow for maximum Listening ability. You attempt never to separate, once contact is established. In certain circumstances, physical separation may nonetheless be unavoidable; but, even, then your mind intent must not separate. In other words, you are expected to do Adhering, Sticking, Connecting, and Following 100% of the time, whether physically touching or not.
The little I have experienced of this kind of interaction is just as CheeFatt describes. From my understanding, a Taijiquan practitioner is not supposed trade punches and kicks with his or her opponent or simply bob and weave to evade strikes. Instead, he or she is supposed to control the opponent’s movements. “Know the other, but do not let yourself be known.” This is a profoundly different strategy from what most martial arts teach and from what most people think of as “sparring.”
Not too long ago, I had a direct experience of this when someone teaching a seminar walked me about a 15-foot square during a simulated, but unchoreographed beating, using only the energy from my feeble attempts at covering up and making sure that I would not end up in the hospital by a misplaced simulated strike. During the 10 to 20 seconds this took, I had no real control over my body placement or position and no effective ability to attack or defend. At times, I could neither fall to the ground nor stand on two legs without the acquiescence of my opponent. My friends later described me as a being played with like a rag doll.
There were many times that we temporarily separated, but he always reconnected. There might have been a few moments when I was in a Qin Na hold, but this was not the primary means of control. What my opponent did was “Adhere” to keep bringing me out of my root, “Stick” to prevent me from opening up “space” to recover, “Connect/Link” to prevent me from being able to turn a corner or effect a reversal, and “Follow” so that I could never seem to get at him or find a way to deny him further energy.
As I understand it, the way to obtain this sort of skill is to become intimately aware of Push Hands energies so that you can feel for them in gradually more difficult and dynamic circumstances. If you opponent has no experience with this, it will be hard for him or her to breach your defenses or withstand your counterattacks, since he or she will not understand what exactly you are doing.