  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.
