The identity and origin of dark matter is one of the more elusive mysteries in the fields of particle physics and cosmology. In the near future, direct dark matter detectors will offer a chance at observing dark matter non-gravitationally for the first time. In this thesis, formalisms are developed to analyze direct detection experiments and to quantify the extent to which properties of the dark matter can be determined. A range of non-standard assumptions about the dark matter are considered, including inelastic scattering, isospin violation and momentum dependent scattering. Bayesian inference is applied to realistic detector configurations to evaluate parameter estimation and model selection ability.
A complete set of simplified models for spin-0, spin-1/2 and spin-1 dark matter candidates are formulated. The corresponding non-relativistic operators are found, and are used to derive observational signals for the simplified models. The ability to discern these simplified models with direct detection experiments is demonstrated. In the near future direct dark matter detectors will be sensitive to coherent neutrino scattering, which will limit the discovery potential of these experiments. It was found that eleven of the fourteen non-relativistic operators considered produce signals distinct from coherent scattering, and thus the neutrino background does not greatly affect the discovery potential in these cases.