The most important thing is the type of encryption being used on the wireless network. The computer has to have the password to that network to log in as well as the type of encryption.
People who don't know a whole lot about wireless often leave their wireless networks with default settings in which case there is no password and it's an open system. To connect to that, just select the SSID (broadcast name) of that network.
The most common type of encryption is WEP. That comes in typically two flavors, a 64-bit or 128-bit encryption. To log into that, you'll need the SSID plus the hexadecimal string that makes up the password. To find that, the router's wireless web admin page will usually show what that password is.
Two more secure types are WPA and WPA2, usually referred to as Personal editions. Lots of older routers won't have WPA or WPA2 as an option, so most of those will use WEP or nothing at all. Enterprise editions of WPA and WPA2 usually require Radius servers that maintain the password. WPA and WPA2 passwords are usually more easily handled as they are typically just character strings that you type in as a password. In both cases, you'll also need the SSID.
Some wireless networks will hide their SSID, usually by unchecking a broadcast SSID option. I've noticed that some wireless clients can't hook up with non-broadcast networks even if the SSID is known. But to connect to this network, the SSID still must be known.
