What are the maintenance steps for PCBs?
The first thing I will say is that for a modern PCB, it will often be impossible to repair in this way. You really need a schematic, and oscilloscope, and an a stereo microscope to really "see" what's going on. Even then it will be difficult unless you designed the board yourself and know exactly how it's supposed to work.

One common exception to this is replacing electrolytic caps. You may be able to repair a PCB by replacing blow capacitors, especially if you're repairing something like an LCD TV where this is a well known procedure.

One other failure that's fairly common that you may be able to fix is replacement of a shorted surface mount component (like a MLCC or diode). I have a special trick for this. You can use this method on boards that have a hard short between power and ground that you can't locate.

First you need some kind of temperature sensor, an IR camera is best, but an IR temp gun or just your finger can work too.

Hook up your board to an adjustable power supply, and slowly increase the voltage until you're flowing 1A or so through the short. Now use your IR camera (or finger) to look for hot components on the board. If you find one, then that will be the failed component.