Experimental search for dark matter must rely on some model which tells us how our instruments, which are made of ordinary matter, interact with dark matter. Otherwise we cannot invent the right instrument to detect dark matter.
The stuff referred to as "dark matter" in current cosmology paper isn't merely matter that is unilluminated or difficult to see ... it's a hypothetical form of ... stuff... that has no interactions at all with normal matter, other than its gravitational effect.
The motivation for postulating dark matter is that our current gravitational equations don't predict sufficiently strong cohesive effects within galaxies to explain their actual observed behaviour, so either our equations are wrong, or there's something else out there that we can't detect except by its gravitational effect.
Currently there's no real model for what this dark matter is or why it should exist, and it's mostly defined by negatives - you can't see it, you can't touch it, it doesn't appear to interact with conventional matter at all (except gravitationally), and it might not even interact with itself (except gravitationally). If it //doesn't// self-interact (except gravitationally) - if it doesn't stick to itself, or clump, or form the dark matter equivalent of solid bodies or self-supported masses - then it might not show any "particulate" behaviour at all, in which case it might even turn out to be modellable as a purely field effect.
Currently it all seems to be a bit nebulous. What we can say, though, is that conventional matter plus the current field equations seems to give the wrong answers, so either current gravitational theory is wrong, or there's some other unknown source of gravitational field out there.
As I understand, most detectors include a dense, massive 'collector' which essentially provides a condensed target for simple collisional interactions with particles that have managed to pass through the Earth and most of the dense detector material. Sensors surrounding the target material are intended to detect emissions produced by the decay of impacted target particles. I think that different impact particles are expected to produce distinct decay emission signals, but I can't add much more. For more complete discussion and references, see http://en.wikipedia.org/wiki/Dark_matter#Detection.
I do not think DM formed by particles which can be gravitationally attracted among them, or from other massive bodies,. I think DM as a massive field integrally anchored to the hot ordinary matter.
There is really only the specific properties that were/are required of dark matter in order to explain discrepancies between observational interpretations of gravitational effects and those expected from gravitational evaluations - i.e., the observed 'flat' rotation curves (velocity|radial distance) of spiral galaxies.
Evaluations of expected properties of particles that might meet those requirements (WIMPs, for example) indicate that they should gravitationally interact, producing increasing densities or 'cuspy' distributions. However, specific observations of some dwarf galaxies whose gravitational evaluations infer the presence of relatively large amounts of dark matter mass indicate that its distribution should be very homogeneous throughout the galaxy.
I think the 'cuspy' halo issue is central to the expectation that dark matter particles should gravitationally interact with ordinary matter, creating higher densities within massive objects, increasing the frequency of detectable annihilations products (gamma rays) within the Sun and galactic center. So far efforts to detect these signals have been unsuccessful.
In summary, there is no one clear model of the conditions that might be likely to produce specifically WIMP detections, but the signals they would generate are distinct for direct and indirect detectors...