Oxygen is carried mostly by being combined with haemoglobin (HHb) to form oxyhaemoglobin (HbO₂).

This occurs in the red blood cells. A very small amount of oxygen is also carried in solution in the plasma. Haemoglobin is a complex conjugate protein made up of four globulin proteins bonded together. Each globulin holds a porphyrin ring compound, haem, which has an iron atom in its structure. The iron atom will combine temporarily with an oxygen molecule. Thus each haemoglobin molecule will carry a maximum of 8 atoms (or 4 molecules) of oxygen. When the oxygen combines with the haemoglobin it releases a hydrogen ion. The hydrogen ion then combines with a hydrogen carbonate ion to form carbonic acid which is converted to Carbon dioxide and a water molecule. The carbon dioxide content of the red cell begins to increase and it diffuses out of the cell and into the plasma. This pathway can only occur in the lung capillaries where there is a high O₂concentration and a low CO₂concentration to ensure flow in  the correct direction. When the red cell is passing by body cells in other organs the O₂ level is low and the CO₂ level is higher so the whole process goes into reverse and CO₂ is converted into hydrogen carbonate and oxygen is displaced from the haemoglobin by the increasing hydrogen ion content of the red cell’s cytoplasm

The movement of hydrogen carbonate ions from the plasma and into the red cell requires the opposite movement of chloride ions to balance the negative ions across the cell membrane. We refer to this movement of chloride ions as the chloride shift. 

The Bohr effect:

The ease with which oxygen  combines with haemoglobin is a measure of the oxygen affinity of haemoglobin, and this affinity for oxygen varies with the oxygen concentration, CO₂concentration and pH. As CO₂ level increases or pH decreases less oxyhaemoglobin is formed at any given oxygen tension....the graph line shifts to the right.

This Bohr shift effect is very beneficial since any tissue which releases CO₂ into the plasma will immediately cause O₂ to disassociate from the haemoglobin to be unloaded into the plasma and then into the cells which need the oxygen for respiration. The more active the cells are, the more CO₂ they release so the more O₂ they cause to be released from the red cells. Supply of oxygen is therefore related to the demand for it in each particular tissue.