We develop a formalism to describe electron ejections from graphenelike targets by dark matter (DM) scattering for general forms of scalar and spin-1/2 DM-electron interactions, and we compare their applicability and accuracy within the density functional theory (DFT) and tight-binding (TB) approaches. This formalism allows for accurate prediction of the daily modulation signal expected from DM in upcoming direct detection experiments employing graphene sheets as the target material. A key result is that the physics of the graphene sheet and that of the DM and the ejected electron factorize, allowing for the rate of ejections from all forms of DM to be obtained with a single graphene response function. We perform a comparison between the TB and DFT approaches to modeling the initial state electronic wave function within this framework, with DFT emerging as the more self-consistent and reliable choice due to the challenges in the embedding of an appropriate atomic contribution into the TB approach.