Siliconera has a nice breakdown on how the touchscreen-exclusive controls will work on the DS. By tapping on the screen, you'll be able to make Mario dribble, with the faster you tap naturally causing him to up the speed of his dribble. While in possession of the ball, swiping the stylus across the touchscreen in the direction of the basket will cause Mario (or whichever subsequent character is holding the ball) to shoot the ball. On the opposite side of the ball, swiping the stylus across the touchscreen in the direction of your opponent will cause your character to attempt a steal on the ball.
Of course, it wouldn't be a Nintendo sports title without crazy power shots and this game does not disappoint. As Mario, in activating your special shot, the game asks you to trace out the letter M on the bottom screen, which will cause Mario to turn up the heat with a flaming basketball. Other characters will have their own unique special shots as well. While I failed to get my hands on it during E3, I'm very excited for this game's release.