The right and left atria pump blood to the right and left ventricles respectively. Under normal conditions, the valves permit blood to flow in only one direction. Blood flow occurs only when there's a difference in pressure across the valves that causes them to open. Blood flows and is pumped from the right atrium across the open tricuspid valve into the right ventricle. These arteries carry blood to the lungs to be oxygenated.
Oxygenated blood is returned to the heart by pulmonary veins.
This oxygenated blood enters the left atrium. Blood from the left atrium flows across an open mitral valve to enter the left ventricle. As the left ventricle starts to contract the mitral valve closes and the aortic valve opens as blood is pumped across it into the aorta. The aorta and arteries that branch from it carry blood to the entire body. The left ventricle is the largest and most forcefully contracting chamber of the heart.