The art of Fault Finding or diagnostics is part knowledge, part skill, part luck, and helped by a lot of experience. And it IS an art, it is something that some mechanics never master and some get very quickly, because it comes down to having an empathy with machines.
That aside, there are some basic tips and rules for fault finding. follow them, and you might not get straight to the nub of a problem, but you will get there in the end. Ignore them, and in all likely hood you'll spend long hours going round in circles not knowing what the problem is, and probably spending a lot of money fixing things that aren't broke.
Now, I will give you a bit of a laugh here. The wife had only been driving a few months, and her car had an automatic choke. Any way, it was a cool morning, and she started the car up on the drive, and the automatic choke did its bit and the car started off running fine. Top of the street, she goes to pull out onto the main road, and the motor had idled long enough to get warm enough to turn the automatic choke off, but not warmed up enough to carburate cleanly, and it stalled.
Now as we live on a hill, after trying a few times to restart the car, flooding it, and draining the battery, she let it roll back down the hill and parked it up outside the house, and scratched her head. Now lets skip forward a few hours, and I get a 'phone call at work. "I think the car has blown up!" So, I get out of work as close to on time as possible, and rush home and don my overalls.
What I find is a car, sat over a puddle of oil that you'd expect to find Greenpeace whallas pulling small birds and rodents out of!
"What did you do?" I asked, calmly, and quietly.
"Well" she explains "When it conked out, the oil light came on, so I guessed it needed oil"
"Right." And I start thinking "So how much oil was in it?"
"Well, I found the cap that you put the oil in, and I couldn't see any, so I put some more in"
"Only a bit!"
"How much is only a bit?"
"Well you had a can of oil in the boot, and it took most of that, because there wasn't much in it, so I got the one out the land rover, and I guess I used about half of that"
Problem solved. It hadn't 'exploded', there was no blown oil seal or con rod hanging through the block, at least not BEFORE she 'fixed' it. All she had done was slug about two gallons of oil into a sump that was only supposed to hold perhaps six and a half pints! In consequence, as soon as she turned the engine over, the pistons came down the cylinders, hit oil and forced it out of whatever orifice it could!
But the question is, LOGICALLY, why would you put oil into an engine that has merely stalled?
In the wife's case, it was because the light with the oil can on it had lit up. Which really goes to show her level of ignorance and the state of panic she was in, more than anything, but also that she never stopped to think or question.
The 3 'Rules'
Take a deep breath. Count to ten. Make a cup of tea. Do anything. But DON'T start trying to find and fix a problem in a hurry. If you are at the side of the road, and you have passengers you'll be harangued with "What's up?" questions as every-one clamours for news. Answer simply, stay calm and weight for the heat of the moment to die away. If you dive in, you wont be thinking straight, and you'll be too flustered to do things logically, and too impatient to do them thoroughly.
OK. We have a problem. What is it? have a look and think what's wrong. Don't try and find the problem or even fix the fault. go backwards. What has happened. What is not working. Don't try and second guess the problem. If you cant get the gear lever to go into gear, don't start thinking 'Gear selectors gone' or if you have no drive 'Clutch has gone', because it might not be, you are jumping to conclusions. Best example, the temperature needle is reading in the red. It doesn't mean the engine is over heating, it means that the temperature needle is in the red! Back up, say what you see. Don't think. Don't jump to conclusions.
Follow the Logic
What are the symptoms? OK, so you have lost drive to the wheels. Engine is running, and there's some funny noises coming from some where, but without jumping to conclusions, what is there between the engine and the wheels that could stop you moving? Clutch, gearbox, transfer box, prop shafts, differentials, half shafts, hubs. Where's the problem likely to be, what can you look at most easily? If the temperature gauge is reading in the red, temperature gauge, temperature sender, wiring. Cooling system. Is the gauge giving a true reading? Has the wire fallen off the sender and been connected back onto the wrong sensor or anything? Is the sender working properly? Is the water hot? Is the fan working? Is there water in the radiator? Is the radiator blocked, inside or out? Is the fan belt tight, could the pump be faulty. Stop and think it through. List ALL the possible causes of symptoms. Look for 'common' causes. Eliminate the easiest / simplest first, and eventually you will find the fault.