Ah, you have MOSFET's, they should call them fuses. :-) (Sounds like it's not blowing your fuses tho, unlike my Sony whose ouput MOSFETS had shortened.
Not quite, the MOSFET's blow your fuses.
I assume you are talking about amplifiers in particular. It's basically just like any other repair.
If it blows fuses, you start at the power supplies. Most amplifiers quite a lot of different voltages. It may be a good idea to find the reason you lost the power first, most times just replacing fuses and blowing hem again does more damage than you started with.
A common problem the safety kicks in. The output relays will be disabled, and if there is a display it will tend to say something like protection. Some amplifiers have LED's or will blink some LED. This commonly means there is DC on the output, and the amplifier is pretending you to blow up your speakers. Mostly means one or more output transistors (and probably the resistors) are blown, or one of the voltages is gone.
If it doesn't start at all check all voltages, and find out why they where gone. Sometimes caps, regulators, bad connections (incl solder joints).
If anything is not working, or not properly, check switches, potentiometers and relays first. Specially with older gear. Specifically relays are difficult to troubleshoot the first time. Normally the sound will work, and at low volumes a channel will distort, of stop outputting audio. You can clean potentiometers or switches, relays should be replaced. If it is not your gear check ALL switches and connections. You won't believe how many amps I "fixed" by enabling the right input, plug the input to the right connection or switching the speaker selection switch.
If you still have problems, check ALL soldering connections, specifically ones that tend to get hot (output transistors, voltage regulators) Re-solder them is necessary. A plastic stick is great for finding bad solder joints. Apply voltage to the device and just poke around carefully.
Sticky brown goo that was used to hold connectors and caps in their place can become conductive after any years.
Maybe this helps as a basic guide
In your case I would do the following:
1. Do NOT power the device with speakers connected. It has NO protection, and DC will kill speakers fast.
2. Check all the voltages
3. If they are OK, put some audio in the amp. Like a sine wave from a PC or function generator. Measure down the schematic, follow the path of the audio, until it stops (check AC AND DC on BOTH channels). Use a sine at it is continuous and easy to measure with your multimeter. Audio will go on and off and is terrible to troubleshoot. It's best not to use a load, as a sine is a quite heavy load for any amp.