What are the mechanisms of ATP synthesis?

The two mechanisms of ATP synthesis are substrate-level phosphorylation and oxidative phosphorylation. 

Substrate-level phosphorylation is a process where an enzyme transfers a phosphate group from a carbon-based molecule derived from food to ADP, creating ATP. During glycolysis and the citric acid cycle, ATP is produced through substrate-level phosphorylation and results in the production of 4 ATP molecules. 

Oxidative phosphorylation is the primary process that generates the majority of the ATP used by our cells, producing up to 27 ATP molecules for each molecule of glucose. Enzymes break down molecules from food, transferring hydrogen atoms (consisting of a proton and an electron) to carrier molecules called FAD and NAD. These carriers transport the protons and electrons to the inner mitochondrial membrane. As electrons move along the electron transport chain, they fuel pumps that transport protons across the inner mitochondrial membrane. These protons then flow back across the membrane through the specialized enzyme F1F0-ATP synthase. This enzyme utilizes the energy from proton movement to synthesize ATP molecules, effectively "charging" them for cellular energy use.