Well, you repair them by finding the issue and then using proper tools and procedures to eliminate the problem..
Seriously, since you are asking the question, you probably don't want to know. Electronics can be extremely complex and you can't possibly expect to fix motherboards by reading a 10-page manual and following some simple instructions. Sure, you may be able to do trivial stuff like replacing capacitors and smaller connectors, but that's pretty much it.
You get tips from these same experienced technicians and you get manuals through the service channel (you work for some big service company that can get technical manuals from the manufacturers).