On the Chevy Corvair you knew it when the engine was dragging on the ground behind you.
Inspection and observation.
Bright spotlight (I love them!), prybar, and a friend should be all you need.
First, visually inspect the motor mounts, then have a friend start the engine and rev it up, let off, rev it up again while you observe the engine mounts and the plates that mount to the block itself--the bolts like to disappear or sheer off from those. Both sides go bad, the DS seems to fail first in my experience from the torquing of the engine.
Pretty much the same for the trans mount. Visual inspection, use the prybar to check for excessive movement. If you want to check it with the engine running while your friend shifts gears put it up on jackstands, and keep away from spinning objects like the driveshaft and tires.
Do you have an issue you are trying to diagnose?