Cellular respiration is the process of oxidizing food molecules, like glucose, to carbon dioxide and water.
C6H12O6 + 6O2 + 6H2O → 12H2O + 6 CO2
The energy released is trapped in the form of ATP for use by all the energy-consuming activities of the cell.
The process occurs in two phases: glycolysis, the breakdown of glucose to pyruvic acid the complete oxidation of pyruvic acid to carbon dioxide and water
In eukaryotes, glycolysis occurs in the cytosol. (Link to a discussion of glycolysis). The remaining processes take place in mitochondria.
Mitochondria
Mitochondria are membrane-enclosed organelles distributed through the cytosol of most eukaryotic cells. Their number within the cell ranges from a few hundred to, in very active cells, thousands. Their main function is the conversion of the potential energy of food molecules into ATP.

Mitochondria have: an outer membrane that encloses the entire structure an inner membrane that encloses a fluid-filled matrix between the two is the intermembrane space the inner membrane is elaborately folded with shelflike cristae projecting into the matrix. a small number (some 5–10) circular molecules of DNA

This electron micrograph (courtesy of Keith R. Porter) shows a single mitochondrion from a bat pancreas cell. Note the double membrane and the way the inner membrane is folded into cristae. The dark, membrane-bounded objects above the mitochondrion are lysosomes.
The number of mitochondria in a cell can increase by their fission (e.g. following mitosis); decrease by their fusing together.
(Defects in either process can produce serious, even fatal, illness.)
The Outer Membrane
The outer membrane contains many complexes of integral membrane proteins that form channels through which a variety of molecules and ions move in and out of the mitochondrion.
The Inner Membrane
The inner membrane contains 5 complexes of integral membrane proteins:
NADH