Troubleshooting is really an art and definitely an acquired skill. Every network has its own particular quirks (just like a used car), and actually maintaining a particular network is the best way to accumulate the information needed to enable you to troubleshoot that network when problems rear their ugly heads.
One way to make troubleshooting problems a little easier is to keep good documentation related to the network. This includes server configurations, network client configurations, and problems that you have experienced and then solved . Even in cases where you are working with a relatively small network, some sort of map that shows how the network cabling has been run and the addressing of the network devices can be a big help in troubleshooting situations.
When actually attempting to solve a problem on the network, try to use a systematic approach to problem solving. First, identify the problem; then gather facts related to the problem. You might want to make a list of the possible hardware and software failures that can cause a particular problem.
Then, systematically go through your list of possible causes one at a time and troubleshoot the problem. This is a much better approach than the "shotgun" approach, where you run around and change a bunch of server and client settings and physical connections all at once. This never allows you to pinpoint the actual cause of the problem. The problem just kind of goes away (because you fixed it with one of the many solutions you implemented). If the problem appears again, rather than immediately being able to provide the correct solution, you will again have to result to voodoo and run through a whole list of fixes.
As you are working through the list of possible problems, you will find that a good, general approach to troubleshooting is to work from the basic to the complex. Check things that will result in a simple fix; for example, make sure the power cables are connected on computers, hubs, and other network devices before assuming the problem is a complex NOS configuration problem with the server. In many cases a disconnected cable or an unplugged hub, rather than a malfunctioning server, will be causing the problem on the LAN.
Troubleshooting basic issues first also allows you to attempt to fix the network without getting way over your head in terms of software and hardware configurations. If you reach a point as you tick off basic issues that could cause the problem where you are in unfamiliar territory, you might wish to call your software or hardware vendor for technical support. There is no disgrace (even for the seasoned network administrator) to try to get help in solving a network problem.