Believe it or not, what separates the three is really quite specific and relates to the temperature of the water or other cooking liquid you're using.
Fortunately, you don't have to measure the water temperature when you're simmering a pot of stock. You can actually distinguish a poach from a simmer from a boil just by observing the steam bubbles that rise to the surface. Learn the definitions of poaching, simmering and boiling.
And while you're at it, here's a more detailed discussion on cooking in hot water or stock that covers all three.