Assuming that there are Weakly Interacting Massive Particles, these particles would then fall out of equilibrium with the universe when they are non-relativistic. One can calculate the abundance of these particles left in the universe today. Their relic abundance is inversely proportional to their interaction cross section. If these particles are to provide the mass necessary to close the universe, their interaction cross section must be of order 10^-38 cm^2. Their mass should be in the range 10 GeV to 10 TeV (proton mass = 1 GeV.) Their scattering cross section is suggestive of weak-type interactions, and they are more massive than "normal" matter -- hence WIMPs.
WIMPs should be gravitationally bound to our galaxy. We can imagine a cloud of WIMPs clumped around the galaxy, with the solar system sweeping through this cloud as we orbit the center of the Milky Way. The WIMPs should have a mean velocity relative to the earth of about 300 km/s. So if we have a detector here on earth, we can try to look for a massive particle scattering off our detector once in awhile, as we move through the WIMP "wind." These particles are very difficult to detect in this way. The more massive they are, the fewer they are, and the fewer scatterings there are.
However, WIMPs occassionally collide with material in the Sun (or Earth) and are scattered so that they are gravitationally captured by the Sun (or Earth) and eventually scatter again so that they become concentrated in the central region. Occassionally a WIMP will collide with an anti-WIMP and annihilate and one of the annihilation products will be neutrinos. We thus expect the Sun, the center of the Earth, and the Galactic plane & center to be the source of WIMP annihilation neutrinos. Detecting these neutrinos may be the best way to search for the TeV range mass.