You cannot use the Xbox 360 Wireless Network Adapter (the black "dongle" that plugs into the back of the console) on a Windows PC.
The Xbox 360 Wireless Gaming Receiver for Windows (white USB dongle) DOES work on PC—it's a different product with signed Windows drivers. It connects up to 4 wireless controllers/headsets.
Summary: The console's network adapter is e-waste for PC use. Buy a proper PC Wi-Fi adapter.