The problem is that Fault Diagnosis of Electronic Devices is a skill in it's own right. In my opinion it's a skill you can't fully teach, it's one you aquire with experience. In the first instance you must obtain a good understanding of Electronics which is 2-3 years in college. After that (and often as part of the Electronics course) you need to gain a good understanding of electronics test equipment.
Once you're at this stage you can be taught some basic fault finding techniques which, when used in conjunction with your knowledge of Electronics theory, can be used to start building your fault-finding experience.
It then takes years and years of trouble-shooting on a daily basis before you can realistically call yourself a good fault-finder. Some people are incapable of becoming a good fault-finder, it takes a certain type of person and a certain method of thinking to be able to do it well!
In short, there's no way we can give you a few simple instructions that will result in you being capable of finding faults on Electronic equipment. Especially not complex digital equipment like the kinds you're talking about.
We can give you an idea of how to do a visual inspection of a board which is the very first thing I and probably most fault-finders would do before they actually do any fault finding, but other than that you're limited to reading a list of common faults and symptoms for the product you're looking at. If you can describe a product and it's symptom we can sometimes offer some pointers on what to check, but even then you're going to need a good understanding of Electronics before you can apply the advice you're given.
Brian