How Oxygen and Carbon Dioxide are transported by the blood.

Oxygen is carried primarily in red blood cells. When oxygen enters the blood stream it binds to iron atoms that make up hemoglobin, which then becomes oxyhemoglobin. Each hemaglobin molecule is capable of carrying four oxygen molecules.
Oxygen has to be transported from the lungs to tissues throughout the body. This means that oxygen needs to bind to hemoglobin in the lungs and then release when it gets to its destination. This occurs due to subtle changes in the pH and temperature of blood, allowing hemaglobin to 'catch' and 'release' oxygen at the right time.
Carbon dioxide is transported by red blood cells but in a different way to oxygen. Red blood cels contain an enzyme called carbonic anhydrase, this enzyme together with water converts carbon dioxide into bicarbonate. Bicarbonate is used to control the pH level of blood and is later turned back into carbon dioxide to be exhaled. Some corbon dioxide is dissolved directly into the blood and some is carried by the hemoglobin molecules but the majority of it is converted into bicarbonate.

References:
www.helium.com/items/763669-the-functions-of-red-blood-cells