A trap many novice troubleshooters fall into is to focus on fixing a symptom rather than cause. If you grazed your knee after tripping on a broken step, would you put a band-aid and keep walking, or would you fix the step? Thus, the best path for successfully troubleshooting a problem is to isolate its root cause through a process of intuition, elimination, and replication.
Listen to your PC
The first thing you need to do is listen to what your PC is telling you. A good doctor will always ask a series of questions before conducting a costly and possibly unnecessary procedure and this applies to your PC. The first indication that something is wrong is often an error message. These can come in two basic forms: Windows specific or application specific. Windows messages often pop up in a box asking you whether you want more information, close the app, or send an error report. Application specific messages can vary greatly in the amount of information they provide.
Unfortunately, most error messages are often far too obscure to be of any use straight away, but they always provide some hint to the cause of the problem. The clues you should look for are things like file or application names, and the type of activity that occurred. This works well for simple problems like, for example, if you try to write to a CD-ROM which produces the error message telling you it can't write to it, but what about error message that don't make sense at all?
A classic example of a confusing error message occurs when you try to delete a file that Windows claims is in use. You know that you aren't using the file, but you can't delete it. Windows isn't lying to you, rather it's just not being terribly clear about what's going on.
So, for this step, glean as much information as you can, and if the error doesn't present itself immediately, you'll need to take a good, long hard look at what's been going on with your system.
History
Most problems on your PC occur because of some change that's occurred in the software or hardware. To kick it off, simply asking yourself what hardware and software you've installed in the last few days. This will often yield the trigger to the problem, if not the cause itself.
Of course, a neat documented history of any changes you've made to your PC would be the ideal option, but it isn't always practical -- especially if you're diagnosing a PC that isn't yours. Windows' System Restore could be the next best thing, as it automatically makes restore points when you update your drivers or perform other significant changes. It's always a good idea to check out the back log before you start troubleshooting.