OK, in tiptronic mode, the gearstick is slid to the left. This then is operated by tapping forward to change up and tapping down to change down. The gearstick is spring loaded so it returns to the central position after each selection, just like the touring cars!
In this mode, you can over ride it and use the paddles and vise verser. Example for me the other day was, taking a corner whilst using the paddles, i was in tiptronic mode and i wanted to change down. As the steering wheel was quite a bit to the left, it was too awkward to use the paddle to change down, so i used the gearstick by tapping it down.
You can again be in drive mode (usually automatic in most cars) and over ride this and start using paddles.
Reference the changing down, in Drive it will automatically do this for you. In Tiptronic or paddles where you control the gears, it will stay in the gear you have selected until the very last minute! Say your in 6th, your just about to stop, once the revs have dropped due to the speed, it will start to change down as it senses that you would be in the wrong gear should you accelerate!
The gearbox also remembers your driving style! If you drive nice and slow for a few days, it will upshift nice and early, if you on the other hand cane it, taking the revs higher, it will remember this and upshift later in the drive mode.
Hope this helps, any more questions, feel free. I also believe that the DSG changes gear in 5 milli seconds!!, using two clutches, one for 1,3,5 gears and the other for 2,4,6 and reverse (think i have that the right way round!!)