In my explanation I mentioned "obvious faults". My first step is a thorough visual (and often olfactory) examination.
How thorough depends on the nature of the fault and the difficulty in disassembling the unit, but examining what you can first with an unaided eyeball, and then under magnification is a good first step.
After you've fixed enough stuff you'll realise that in some significant number of cases, when you've found the fault, there was at least some physical indication. I spent some time figuring out how a front panel worked before finding a crack in a PCB I should have seen earlier.
Note: text below in grey was autocorrected to an extent that I can't figure out what I meant. I would normally correct it, but even I'm lost this time.
The other thing I failed to mention is getting a fault history. Did this happen after dropping, after lowering was dropped ok it, after years of no use, with a pop and smoke, after shorting the output, after the wrong adapter was plugged in, etc. And has someone else tried to fix it?
And prepare yourself with all the documentation you can find, with schematics if possible. Are there any days finding guides, descriptions of operation, service manuals, block diagrams, or even you tube videos of people fixing it. Oh, and any forums where people have discussed it. Google is your friend in most cases. Otherwise, perhaps the manufacturer, or even an old employee or someone who has maintained then in the past can help you.
If, as in the case of a piece of equipment I looked at a while ago, the device still functions to some extent, make sure you understand exactly what does and doesn't work. That can point you toward where to start (probably after you confirm the power rails are ok).
