If you hear an onion ring, please answer it. The chicken came first, God couldn't lay an egg. The fact that it's an electromagnetic wave means that at any point, there's an electric field and a magnetic field exerted in a certain direction, which then reverses direction as the wave passes.
Any substance is made up of atoms, consisting of a nucleus and electrons floating around it.
Since the electrons aren't attached, they can be pulled around a bit by an electric field. Since light is an electromagnetic field, when light hits a particle, the electrons are wiggled by the light. So an oscillating electric field acts as a transmitter. The particle takes some of the energy from the light wave in order to get the electrons oscillating, and then retransmits it at the same frequency - in all directions. At this point, it's the size of the particle that's important.