Weakly interacting massive particles (WIMPs) are among the leading dark matter candidates. Currently, the most promising method for detecting many different WIMP candidates is the direct detection of the recoil energy deposited in a low background laboratory detector due to elastic WIMP–nucleus scattering. So far the usual procedure has been to predict the event rate of direct detection of WIMPs based on some model(s) of the galactic halo. The aim of our work is to invert this process. That is, we study what future direct detection experiments can teach us about the WIMP halo. As the first step we consider a time-averaged recoil spectrum, assuming that no directional information exists. We develop a method for constructing the (time-averaged) one-dimensional velocity distribution function from this spectrum. Moments of this function, such as the mean velocity and velocity dispersion of WIMPs, can also be obtained directly from the recoil spectrum. The only input needed in addition to a measured recoil spectrum is the mass of the WIMP; no information about the scattering cross section or WIMP density is required.