Question

How does light determine whether it acts as a particle or a wave?

Answer 1

Light doesn't need to decide. It simply behaves both ways at the same time.
If you create an experiment that can detect particles and run light through it, the experiment detects particles.
If you build an experiment that can detect waves and run light through it, the experiment detects waves.
Wierd but true.

Answer 2

Great question. Albert Einstein proved that light acts as both a particle and a wave in his 1905 paper. This is called wave-particle duality.
With quantum mechanics, it is easy to prove that light behaves as both a particle and a wave.
When UV light hits a metal surface, it causes an emission of electrons. This "photoelectric effect" proves how light behaves.