How we will describe the whole mechanism of fish breathing under water? How they absorb oxygen and and then remove oxygen through a process known as gas exchange?
Fish are able to obtain oxygen that is dissolved within the water, and exchange it along with Carbon Dioxide through their gill structure, called filaments. The gills are located adjacent to the mouth and filaments include a large amount of blood vessels. Those blood vessels (capillaries) are close to the gill filament surface and move in the opposite direction to the water flow, which they are exposed to by means of the fish drawing in water through it's mouth. The tissue that comprises the filament is porous and allows for diffusion of these small molecules (oxygen and carbon dioxide) across this tissue and into the blood vessels. Each red blood vessel consists of four "Heme groups," which are designed exclusively to bind to oxygen and transport it through the body. A process called the Root effect (Bohr effect in other vertebrates) in hemoglobin regulates the "drop-off" of oxygen by recognition of low pH values.
Hughes, G. M., & Morgan, M. (1973). The structure of fish gills in relation to their respiratory function. Biological reviews, 48(3), 419-475.
Bonaventura, C. E. L. I. A., Sullivan, B., & Bonaventura, J. (1976). Spot hemoglobin. Studies on the Root effect hemoglobin of a marine teleost. Journal of Biological Chemistry, 251(7), 1871-1876.