You start with posting all you can find about your mower
Mower brand model number & serial number as found on the ID tag
And the same for the engine
Then you get your hands on the wiring diagram for your mower
After that you peel back the insulation at every plug & terminal and take a photograph, actually several photographs so you know which wire went into what position in what plug
Now you start cutting off the insulation but as you do you use twist ties or reuseable zip ties to keep the wires together and very importantly each side of where a wire exits the main loom, and all the time photo , photo , photo & even more photos
You will also need to remove the blower housing & flywheel to visually examine the stator
Then you look at the damaged wires, where the damage stated, where it ended & what wires are damaged
These will point towards what failed & where it failed
If you are lucky it will be just a couple of wires
The engine can be started with a jumper independent of the mower to check the regulator / rectifier if necessary.
When you know which wiring diagram is correct for your mower, print it out as big as possible. even if you have to go to an instant print shop and pay for a couple of prints.
I print most out in A2 size ≈ 24" x 32" and if they are not in colour I use coloured pencils or textas to over colour them so everything is easy to see
During normal running there are only 4 mower wires that have power flowing through them
1) power feed to mower from battery
2) power feed from alternator back to the battery
3) power feed to electric clutch
4) power feed to carb solenoid
All the other wires are ground wires and as such if they short to ground nothing happens to the loom ( mower might not run though )
And usually it will be numbers 1 or 2 as the PTO generally has a 5A or 7A fuse on it which will blow way before any wire gets hot enough to melt the insulation
So there is a start
As you have been warned, it will be a long & tedious task at best
If you are not bald now you will be when you have finished
We are here to help you if you want to tackle it yourself but it will usually be several weekends worth of work & your grass will not oblige by mowing itself .
The only times I have replaced a complete loom was because one customer wanted the mower fixed RIGHT NOW & did not care about the cost which was just under $ 1000 ( Aus ) and for the commercial customers where the mowers had done big hours & nearly every wire had hardened & broken off at the crimp terminals