Well, there are many gas exchanges we could describe, but I will assume you are talking about the one that takes place when we breathe. When you take in a fresh breath of air, that air enters the nose or the mouth, and follows a tube called the trachea, or windpipe. The trachea branches off into two separate tubes called bronchi, which enter each of the two lungs. The bronchi branch off into smaller tubes called bronchioles, with each bronchiole leading to grapelike clusters of air sacs called alveoli. It is in the alveoli that the gas exchange takes place. Surrounding each alveolus is a capillary, the smallest blood vessel. The walls of the capillaries are so thin the oxygen can diffuse directly into the blood, where it attaches to the heme molecule in red blood cells. The red blood cells take the oxygen to every cell in your body, where it is utilized in a process known as cellular respiration, where it produces energy for the cell to do it's life processes.
The carbon dioxide that is produced as a waste product from cellular respiration must be eliminated from the body, so the carbon dioxide attaches also to the heme molecule in the red blood cells, which then go back to the alveoli in the lungs. The process described above takes the reverse in the order of steps, and you exhale carbon dioxide.