It is a while since I fixed a lot of SMPS.
In those days they mostly used bipolar devices.
That said, the way we looked for short circuits was using a DMM on the Ohms (not "continuity") range, with obviously, no power applied to the circuit.
A good idea is to disconnect the later sections of the circuit, & starting from the ac Mains input, check for shorts firstly between Active ("hot) & Neutral, & then if that looks OK, between the + & - outputs from the bridge rectifier.
If there is a "short" there, disconnect the switching part of the PSU, & check again.
If it now looks OK, you have narrowed the problem down to the switching part.
This is where it gets messy-----maybe the active device/s involved are faulty, or some of the passives around that area.
If, however, you don't see a "short" anywhere on Ohms range, but the thing blows Mains fuses or smokes when powered up, you may have something like a shorted turn in the switching transformer.(Sony call it a "choke" but if it looks like duck, quacks like a duck....)
This will usually kill the main active device, though!
No doubt there are things I have missed, like there being a huge load on the secondary of the switching transformer, which might give similar results to a short at the input.
No one can give you a generic "road map" through SMPS faultfinding that will address every possible situation.