Is your usb cable inserted in the right usb port. I know that sounds funny, but my computer has two usb ports on the front, but for some reason some things only work when they are in a certain port. If you turn the volume up, and if your computer is like mine, when you plug the usb cable in your computer should make a noise, like a chime, that means that a connection was made. After that is done, your Action Replay DS should connect with your computer and the list of codes on the card should show up in the left panel of the window. It will do this automatically, you don't have to (at least normally) select anything via the DS screen inputs.
If you haven't already you should try checking to see if newer updates are available. You do this by clicking on the DS card icon in the top right corner, (the DS system icon will just rewrite your AR to all the current codes and that takes a long time as it erases all the codes already on the card and rewrites them).
But, once you have it connected via the included usb cable (unlike the code breaker DS, the AR doesn't use the DS's wifi to update the code list, AR you need to use the usb cable.) your AR's code list should show up on the left panel.