My iPhone 5c is stuck after attempting to upgrade software

My screen is black and reads "support.apple.com/phone/restore" at the top. It has a picture indicating I plug it into my Mac. I have it plugged in however, the iPhone does not appear in my finder or on my Mac Screen, as I thought it would after following the directions. I have held down the volume buttons and the on/off button, as well, but nothing. What else can I do to get it to start working?