High performance batteries based on the movement of Li ions in Li x CoO2 have made possible a revolution in mobile electronic technology, from laptops to mobile phones. However, the scarcity of Li and the demand for energy storage for renewables has led to intense interest in Na-ion batteries, including structurally-related Na x CoO2. Here we have determined the diffusion mechanism for Na0.8CoO2 using diffuse x-ray scattering, quasi-elastic neutron scattering and ab-initio molecular dynamics simulations, and we find that the sodium ordering provides diffusion pathways and governs the diffusion rate. Above T ~ 290 K the so-called partially disordered stripe superstructure provides channels for quasi-1D diffusion, and melting of the sodium ordering leads to 2D superionic diffusion above T ~ 370 K. We obtain quantitative agreement between our microscopic study of the hopping mechanism and bulk self-diffusion measurements. Our approach can be applied widely to other Na- or Li-ion battery materials.