Every electrical fault falls into one of two families, and they behave like mirror images of each other. Learn the signature of each and a multimeter turns fault-finding from trial-and-error into a straightforward trace.
The open circuit
An open is a break in the current path - a blown fuse, a broken wire, a failed component, a switch that won't close. With no path for current, resistance across the open reads infinite (OL on a meter in ohms mode). Voltage tells the more useful story: since current can't flow anywhere, there's no voltage drop across any of the good components - all of the supply voltage piles up across the single open point. A component that should be closed but shows full supply voltage across it is showing you exactly where the break is.
The short circuit
A short is the opposite: an unintended low-resistance path, from a wire touching a chassis, insulation breaking down, or a dropped conductive tool. Resistance across a short reads near zero. Voltage across it reads near zero too, for the same underlying reason - there's essentially no resistance there to drop voltage across. Current, meanwhile, spikes toward infinity by I = V/R as R approaches zero, which is exactly what upstream fuses and breakers exist to catch.
Reading a blown fuse without pulling it
A blown fuse tests OL in resistance mode - it's open, so no surprise there. But you can also test it live: measure voltage across the fuse in a powered circuit. Full supply voltage across it means it's blown (it's the open). Near-zero voltage means it's good (minimal resistance, minimal drop). One caveat worth remembering: a fuse can test fine in resistance mode and still fail intermittently under load - if you have doubts, replace it rather than trust a single clean reading.
Working a live circuit safely
To trace an open in a live ladder circuit, start at the load and work back toward the source, checking voltage across each series element in turn. The first element that shows full voltage is your open fault - everything downstream of it reads 0V, because no current is reaching it to produce a drop. With the circuit de-energized instead, resistance mode does the same job: OL means open, near-zero means a good low-resistance path, and a value in range means a healthy resistor. One firm rule either way: never put an ohmmeter on a live circuit. Its internal battery supplies the test current, and an energized circuit will overwhelm it - and possibly destroy the meter.
Phantom voltage, backfeed, and the full fault-diagnosis toolkit are covered in the Study Guide, with practice problems in the Exam Companion.