Ash is detected by flight crews using the following:
A smell of sulphur, or burning.
A red glow in the engine intakes.
High EGT/TIT.
Vibration.
Abnormal pitot/static instrument readings.
The immediate response is to close the throttles and turn 180 degrees to leave the area. When clear, add enough power to remain airborne until sure you are clear of all ash.
The ash will pass through the engine with minimal damage if the engine is at idle because the temperatures are not high enough to melt it. Continuing to run at settings higher than idle will maintain the temperatures.
You will also have ash damage to leading edges, pitot tubes, windscreens and the like, depending on the amount of ash and its contents.
Not all ash clouds will be forecast. Any cloud might contain ash, especially when flying the Ring of Fire (and near Iceland!).