Respiration is a cellular process which occurs in each and every cell of body. It starts with glycolysis- a reaction in which breakdown of glucose occurs. Glucose gets converted into pyruvic acid. The process of glycolysis takes place in cytoplasm.
Now this pyruvic acid enters into mitochondria via link reaction in which it gets converted into acetyl-CoA. Now this acetyl-CoA enters in the mitochondria where it performs kreb's cycle in mitochindrial matrix. All the ATP and NADH2 and FADH2 produced till now performs ETS cycle (Electron transport chain) which is located in the mitochondrial membranes. Finally it undergoes oxidative phosphorylation and ATPs are released.

GLYCOLYSIS(in cytoplasm) → LINK REACTION(in cytoplasm) → KREB
CYCLE(mitochondrial matrix) → ELECTRON TRANSPORT SYSTEM
(mitochondrial membrane) → OXIDATIVE PHOSPHORYLATION(mitochondrial membrane).