Presumably the "Wireless Network Adapter" is a PCI card in a desktop PC?
If so, you would go into Device Manager, expand the Network adapters section, highlight the wireless adapter and click the button to uninstall it.
Then shut down the PC, open the cover and (taking anti-static precautions) remove the PCI card. It will be held in place with a single screw and can then be pulled out.
Plug it into a spare PCI slot in the new PC, boot, let Windows find new hardware and use the drivers CD that came with the card to install it. Once installed, it will be listed in Device Manager and you will have an entry in the Network Connections folder for a "Wireless Network Connection".