You just select Sport Mode. Use the appropriate paddle when you would normally upshift or downshift a real manual/dual clutch transmission, and the car's computer will simulate shifting gears. If you screw up too badly, the computer will take over, and change the gear ratio itself.
Anonymous got it right: it's basically a video game, but you're actually driving a real car. The whole reason for the system is people see Ferraris and Aston Martins on TV, and go "I want that feature in my Ford Focus." The difference is that on a regular car, it's fake.