As mentioned above, you will have a much better chance of success if you have a plan going into an electrical problem. Here's what I normally do when dealing with an electrical issue.
First, a good inspection. I start at the battery. If it looks old or corroded or has loose terminals, I deal with that first. I know not all electrical issues are the result of battery issues, but considering its importance in the electrical system, it's worth at least a glance when you open the hood. If you suspect an issue, check the surface voltage, load test it, clean up, and deal with any battery terminal issues you might have.
Next, check all the fuses — and I mean all the fuses. I can't tell you how many times I've fixed an electrical issue just by replacing a fuse. If that same fuse continues to blow, you need to look further into that. Most times if there’s a recurring problem, the new fuse will blow almost as soon as you put it in. If it doesn't, activate the affected system and check its operation. If it's good, monitor it until you feel confident it's not going to have a problem again.
If you do have an electrical problem, find a wiring diagram for the affected circuit. Without it, you're lost. The best wiring diagrams, in my experience, are put out by the manufacturer. Do what you can to get your hands on one of those when dealing with an electrical problem.
Once you have the wiring diagram, study the circuit. See if you can figure out what the issue is before you even go to the vehicle to do your testing. It is possible to do this with a bit of practice and the ability to read a wiring diagram. Sometimes you can look at the diagram, find related circuits that might be affected, test those, and find the problem through a process of elimination. This is really where your plan gets put to use.
I like to start at the load when checking for electrical problems, especially with 12V systems. I do this especially if the load is easy to get to. What I mean by load is the component(s) the circuit controls. In the case of a cooling fan circuit, the cooling fan is the load. All the other controls of the circuit are there to control the operation of the fan, or load. I do this because I often find it's the load itself that's failed. I also do this because the load is sometimes more accessible than the wires or controls going to it. I can unplug the load and check for power and ground to the component.
If I don't have either one of those, I know where to go next. If I do have those, I check the operation of the load itself. If it's a cooling fan, I run power and ground directly to it to see if it can operate on its own. If not, I know it's bad and I can replace it.
If it does work, I've got more investigating to do. Sometimes you can have power and ground in a circuit and it's not enough to work the load. This can be due to a short circuit or increased resistance in the circuit somewhere. Once again, we go back to the wiring diagram to try to figure out where that might be and come up with a plan for testing the suspected part of the circuit.
Once you're done finding and repairing the problem, verify your work. Make sure everything works like it's supposed to. This way, you can avoid having to deal with it again in the future.