Beginning with a set of simplified models for spin-0, spin-$half$, and spin-1 dark matter candidates using completely general Lorentz invariant and renormalizable Lagrangians, we derive the full set of non-relativistic operators and nuclear matrix elements relevant for direct detection of dark matter, and use these to calculate rates and recoil spectra for scattering on various target nuclei. This allows us to explore what high energy physics constraints might be obtainable from direct detection experiments, what degeneracies exist, which operators are ubiquitous and which are unlikely or sub-dominant. We find that there are operators which are common to all spins as well operators which are unique to spin-$half$ and spin-1 and elucidate two new operators which have not been previously considered. In addition we demonstrate how recoil energy spectra can distinguish fundamental microphysics if multiple target nuclei are used. Our work provides a complete roadmap for taking generic fundamental dark matter theories and calculating rates in direct detection experiments. This provides a useful guide for experimentalists designing experiments and theorists developing new dark matter models.
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