If the StarSense hand controller has the mini USB connector you will NOT require a USB-serial adapter. Only as mentioned a simple USB mini to A connector cable. There is still a serial component involved but the USB-serial adapter is built into the hand controller, so you will need the correct device driver for the Prolific chipset used but you won't need any other hardware but the USB cable.
If the StarSense hand controller has the small RJ connector on it's base then you WILL need the Celestron hand controller serial cable (#93920, or equivalent) and an RS232 serial port on your PC. For most folks this will be a commercial USB-RS232 serial adapter and the appropriate device driver for the chipset used in the adapter.
More detail on this is available on Mike Swanson's website www.nexstarsite.com