Neutralino annihilation and elastic scattering cross sections are derived which differ in important ways from previous work. These are applied to relic abundance calculations and to direct detection of neutralino dark matter from the galactic halo. Assuming the neutralino to be the lightest supersymmetric particle and that it is less massive than the Z sup 0, we find relic densities of neutralinos greater than 4 percent of critical density for almost all values of the supersymmetric parameters. We constrain the parameter space by using results from PETRA (chargino mass less than 23 GeV) and ASP, and then assuming a critical density of neutralinos, display event rates in a cryogenic detector for a variety of models. A new term implies spin independent elastic scattering even for those majorana particles and inclusion of propagator momenta increases detection rates by 10 to 300 percent for pure photinos. Z sup 0-squark interference leads to very low detection rates for some values of the parameters. The new term in the elastic cross section dominates for heavy, mostly spinless materials and mitigates the negative interference cancellations in light materials; except for the pure photino or pure higgsinos cases where it does not contribute. In general, the rates can be substantially different from the pure photino and pure higgsino special cases usually considered.