A book will help you understand all the computer names and parts in theory, but when you sit in front of a computer, it is a different game.
First thing you should do is disable the IT person's account, so he can't get into the computer and mess around with the network. Next, I would get all the documentation on the infrastructure including the settings on the servers, which may include the password, ip address, email account information and how active directory was set up.
If the IT individual has excellent documentation of the network and overall infrastructure, your job just became a little easier. If the individual did not document any of it, then you should spend time gather information of each computer, like their computer name, ip address, location and the person who uses that computer. This can be an easy task if you use an application that will obtain a list of computers by IP address, but it will not tell you their location in the building. Check out this website for possible freeware products:
MajorGeeks.com - Download Freeware and Shareware Computer Utilities.
Now, all computers look like they are running great, but check out event viewer because this area will have logs of what is going on with the computer. The application and system log will display information, warnings and errors. If you notice a ton of errors, then you should try to fix them by either googling the event id number and name, or you can go to
EventID.Net - Troubleshooting information for Windows event logs, which is a fantastic website that will give you information on the problem.
To look at event viewer, right click on my computer, left click on manage and new window will pop up. Double click on event viewer and you will see the application, Internet exploer, security, and system logs. Click on each one and view the information.
If you want to read a few books to learn about computer or network problems, I would recommend going to amazon and going to their computer book section. If the server runs Windows Server 2003, then find books talking about the OS.