Summarize:

Take a chef's knife and lay it on the clove so the flat side is resting on top of it. Hold the knife handle with one hand and bring the palm of your other hand down on the flat blade. The pressure of your palm will smash the clove. You don't need to flatten the clove of garlic as you smash it. Just apply enough pressure to loosen the peel.
Push the flat side of a knife on the clove to loosen the peel.