Nickel exhibits promising catalytic activity for dissociating CO₂ to CO via the reverse water-gas shift reaction or to methane through Sabatier reaction, as reported in recent experiments on both Ni(111) and Ni(110). Despite numerous experimental and theoretical studies, the mechanism of the CO₂ hydrogenation is not yet fully understood. We have investigated the mechanism of reducing CO₂ on the Ni(110) surface in the presence of the subsurface or impinging hydrogen using spin-polarized periodic density functional theory and Born-Oppenheimer molecular dynamics simulations. In the case of the subsurface H atoms, they act as both spectator species and reactants of the reactions and hence provide the extra energy for overcoming the reaction barriers, in which the major contribution comes from the energetics of subsurface H emerging to the surface as a reactant. In the case of the impinging hydrogen, the simulation results show direct theoretical evidence for both associative and redox mechanisms in the reaction of atomic hydrogen with CO₂. Because H₂ is dissociatively chemisorbed on Ni(110) with nearly unit probability, the mechanisms are also relevant to the reverse water-gas shift reaction (H₂ with adsorbed CO₂). Furthermore, we provide the first real-time demonstration of both Eley-Rideal and hot atom mechanisms when H impinges on adsorbed CO₂.