How do oxygen and carbon dioxide get exchanged in the air sacs of the lungs?

Deoxygenated blood that has just returned from the tissues of the body and the coronary circulation (the system that provides oxygenated blood to the tissue of the heart itself) enters the right atrium of the heart.  From there, it will be pumped through the tricuspid valve and into the right ventricle.  The ventricles contract and the blood travels from the right side through the pulmonary trunk and artery to the lungs.  From the pulmonary artery, the blood makes its way to the capillary beds surrounding the alveoli (air sacs) of the lungs.  This is where gas exchange takes place.

The gases being exchanged are oxygen and carbon dioxide.  When gas exchange occurs, it is important to remember that each gas must be considered separately (the diffusion of one gas will not be influenced by another gas--Dalton's law) and that gases will diffuse from high partial pressure to low partial pressure.  

The cells that make up our tissues utilize oxygen for metabolic processes and produce carbon dioxide as a byproduct so blood that is returning from the tissues and making its way to the lungs has a relatively high partial pressure of carbon dioxide (45 mmHg) and a relatively low partial pressure of oxygen (40 mmHg).  The air that has just been inhaled and is entering the alveoli of the lungs is the opposite, the partial pressure of oxygen is relatively high (105 mmHg) and the partial pressure of carbon dioxide is relatively low (40 mmHg) due to their concentrations in atmospheric air.  

Considering each gas separately (Dalton's law), all you have to do is compare the partial pressures of each gas across the membranes.  The membranes between the capillaries and alveoli are simple squamous epithelium so diffusion will occur readily.  Carbon dioxide's partial pressure is higher in the capillaries than in the alveoli so the carbon dioxide will diffuse from the capillaries and into the alveoli where it can be exhaled.  The partial pressure of oxygen gas is higher in the alveoli than in the capillaries so the oxygen will diffuse from the alveoli and into the capillaries.  The blood is now oxygenated and will return to the left side of the heart and then to the body (systemic circulation) where oxygen can be delivered again to the tissues.