In the video below, it seems like you can navigate titles using the DPad, the left analog stick or even by swiping the touchscreen. There are even more ways to flip pages back and forth. In addition to how you browse titles above, you can also use the L and R trigger to navigate left and right. You can zoom to focus your reading on every cell and you can also read on vertical orientation.
We didn't really get the chance to go to Tokyo and experience this first hand. Destructoid on the other hand had a few things to say about the app. They say that because of the sharpness of the images displayed on the Vita's OLED screen, it's as if you get a popping-out effect.
The reader app and online store will be available on October 2012 in Japan with over 3000 manga available at launch.