Normally, a Wireless Network Adapter will connect automatically to the wireless network when the PC is booted, provided the network is available.
However, if the option to "Disconnect" has been used, connection will no longer be automatic. It is necessary to go through the routine to "Connect" again, i.e. 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.
There is a difference between the Wireless Network Adapter and Router communicating with a good signal and "Connecting" (as in "logging in") to your Wireless network.
Once "Connected", and provided the option to "Disconnect" isn't used again, future connections will again be automatic.