1) Remove the existing "profile" that has been saved within your wireless settings and which is used to connect automatically to your wireless network when it is available.
2) Enable broadcasting of your router's SSID.
3) "Connect" to the network. In other words, run the wireless adapter's software, scan for "Available Wireless Networks", find and highlight the one that matches your router's SSID (network name) and select the option to "Connect" to it. You should be prompted to enter any WEP or WPA encryption key and, once "Connected", the wireless adapter should get its IP address by DHCP from the router and you should have network and internet access.
4) In the "Properties" of the connection, ensure the box is ticked for "Connect even if this network is not broadcasting".
5) Re-hide the SSID.