The three stages of cellular respiration are glycolysis, the Krebs cycle and the electron transportation system. These stages are associated with aerobic respiration, which requires oxygen. The other type of respiration, anaerobic, doesn't use oxygen.
Glycolysis is the first step and involves the oxidization of glucose, which causes it to break down into three carbon molecules. One carbon molecule is removed as waste. The second process is the Krebs cycle, where the two remaining carbon molecules undergo a series of reactions. The final process is the electron transport system where energized electrons harvest adenosine triphosphate. Oxygen is important to this process as an electron acceptor.