The Joint Push/Pull tool operates by allowing users to select a face or a group of faces and then define a push or pull direction. This direction can be based on an existing edge, axis, or even a guide line. Once the direction is established, users can input a specific distance or offset value to push or pull the selected faces. This tool also supports the use of inference engines, which help in snapping to specific points or axes, thereby ensuring precision and alignment with the rest of the model.