On the new SHIELD TV, you can enable the USB port furthest from the HDMI port to connect to a PC using a USB type-A to USB Type-A cable.
Enable this feature in Settings -> Storage & reset. Select "Using USB" under "SHIELD Storage access". Note that when this feature is enabled, you can no longer use the port for other needs.
On SHIELD TV Pro and SHIELD TV (2015), the micro-USB port must be used to connect SHIELD to a PC. Use the included micro-USB to USB cable.