in what organelle does this process happen

The process you’re referring to occurs in the mitochondria. Specifically, cellular respiration takes place across several mitochondrial sub- compartments: glycolysis happens in the cytoplasm, while the pyruvate oxidation and the citric acid cycle occur in the mitochondrial matrix, and oxidative phosphorylation (electron transport chain and ATP synthase) occurs in the inner mitochondrial membrane (cristae) [source: standard cell biology references]. If you’d like, I can tailor the answer to a particular organism or provide a brief diagram-like description of which steps happen where within the mitochondrion.