Rinse the artichokes. Rinse each artichoke under cold running water, gently spreading the leaves so water can reach between them. Shake off the excess water.
Trim the stems. Use a sharp knife to cut each stem to approximately 1 inch long.
Trim the leaves. Use kitchen shears to snip the thorny tip from each leaf. This makes the artichokes easier to handle and eat.
Cut off the tops. Use a sharp knife to cut approximately 1 inch from the top of each artichoke.
Fill the pot. Pour 3 to 4 inches of water into a large pot. Add the artichokes, bay leaf, garlic and a few lemon wedges. The artichokes will not be completely submerged, and that is okay.
Boil the artichokes. Cover the pot and bring the water to a boil. Reduce the heat to medium-low and cook, still covered, for 30 to 40 minutes.
Check for doneness. Pull gently on an outer leaf. The artichokes are done when the leaf releases easily and its fleshy base is tender. A sharp knife should also slide easily into the base of the artichoke.