Connect the amp to a power source with inline fuse {fuse chosen depends on the amp}, then turn it on with no input or speaker connected. If the fuse blows, the amp is toast. Or, if the fuse doesn't blow *and* the amp has a protect light = on.
The other method is to poke around inside with a DMM and check for shorted power transistors with
nothing connected to the amp, no power, ziltch.
What causes an amp to blow up? You can make a huge list.
* power supply input voltage exceeds specs.
* speaker load lower than specs.
* overdriving the amplifier so it outputs high power.
* poor cooling.
* wiring error.
* bad luck, electronics will fail with no reason.
* lending your car to a friend who said "Really, I didn't turn up the stereo".
* bad design