As the others are saying, one method is to understand exactly how the circuit is supposed to work, and then use methods such as signal tracing to track down the problem. This is a very difficult approach because it takes a lot to learn exactly how a board is supposed to work. There are other simpler approaches that can sometimes be helpful though. One way is to guess that there is a bad solder joint somewhere on the board and then re-solder every connection on the board. Its a lot of work, but can be successful in some cases. I have had some success with this approach in consumer audio gear, especially car radios. Another way is to identify the power supply traces on the board and measure those to see if they have voltages that make sense. Power supply failure is a common type of fault and just checking power supply voltages with a meter can help track down such problems. Another way to find faults on a board is to inspect it very closely, preferably using a stereo microscope. Look for burned components or traces, broken capacitors, cracked solder joints and cracked traces, loose wires, and basically anything that appears to be not quite right. Another technique that can be useful is to substitute modules or sub-assemblies to try and find which is faulty. This can be helpful to narrow down the problem in items that have more than one board or module.