Adding a Computer to a Home Network
The easiest way to add a computer to a home network is by switching it on and waiting for the wireless card to detect the network.
Once the network has been detected, you will need to enter the security credentials in order to utilize the connection.
However, this is the best case scenario. Your network or PC might not be wireless, requiring you to connect to your router via an Ethernet cable. Once this has been done, however, your PC operating system should detect a new connection which you can then use. (Note that if you intend to use the internet, you will need to change settings in your browser to use this new connection. The easiest way of doing this is to use Internet Explorer and go to Tools > Internet Options > Connections > LAN Settings and check the box labelled Automatically detect settings.)
Alternatively you might be trying to add a computer to a hidden network. These types of network are used to maintain privacy, and require that new devices know the network name, security type in use (for instance WPA, WEP, etc.) the encryption type and the security key. A new network connection can be setup from your PC to take advantage of this. For instance in Windows 7, go to Start > Control Panel > Network and Internet > Network and Sharing Center > Set up a new connection or network > Manually connect to a wireless network.