In regions of very high dark matter density such as the Galactic centre, the capture and annihilation of WIMP dark matter by stars has the potential to significantly alter their evolution. We describe the dark stellar evolution code DarkStars, and present a series of detailed grids of WIMP-influenced stellar models for main sequence stars. We describe the changes in stellar structure and main sequence evolution which occur as a function of the rate of energy injection by WIMPs, for masses of 0.3-2.0 Mo and metallicities Z = 0.0003-0.02. We show what rates of energy injection can be obtained using realistic orbital parameters for stars at the Galactic centre, including detailed consideration of the velocity and density profiles of dark matter. Capture and annihilation rates are strongly boosted when stars follow elliptical rather than circular orbits. Dark stars are unlikely to exist on any circular orbits in the Milky Way. If there is a spike of dark matter induced by the supermassive black hole at the Galactic centre, solar-mass stars following orbits with periods as long as 50 years and eccentricities as low as 0.9 could be significantly affected. The observation of low-mass stars on such orbits would either provide a detection of WIMP dark matter, or place stringent limits on the combination of the WIMP mass, spin-dependent nuclear-scattering cross-section, halo density and velocity distribution near the Galactic centre. In some cases, the derived limits on the WIMP mass and spin-dependent nuclear-scattering cross-section would be of comparable sensitivity to current direct-detection experiments.