In most communities the library signal is free to the residents to use. The school's is most likely not. Being only a few doors away, you might be able to pick up either signal in your home but it may be weak. You connection will also be slower at peak usage times because you will be sharing your access with everyone else using it.
You can check your wi-fi enabled Vista computer to see if it detects the library's network by clicking on Start and then Connect To. This will open a window with a list of wireless access points. I can see 5 in addition to my own. All of them are secured so only my network is available to me. Your library's network is probably unsecured. You can connect to an unsecured network by clicking on it to highlight it and then click on Connect.
Please don't add your computer to a neighbor's unsecured network. Just because someone has not taken the steps to secure their network that does not mean that it is there for the taking. That would be like borrowing someone's car because they left the key in the ignition.
Like others have said, using an unsecured network opens you up to sharing your files with others on the network unless you take the precautions to keep your files private. Make sure that you have any file sharing turned off.
Another drawback would be that if the library is closed, they may also shut off their network. So you may not have access during the late night, on Sundays, holidays or early morning hours. It's something to think about if you enjoy surfing the web at those times.