What version of iTunes do you have on your computer. You need iTunes 10.7 or later with iTunes 11.0.1 being the current version. Also iTunes 11 changed how iTunes looked. To make it appear more like what you saw in earlier versions of iTunes use the View menu to view the Left Sidebar.
If you still do not see your device listed reboot your computer. Then reset your device like this:
Press and hold the Home and Sleep buttons simultaneously ignoring the red slider should one appear until the Apple logo appears. Let go of the buttons and let the device restart. See if that fixes your problem.