There are many searches now underway for the dark matter. 

For MACHOs, the most promising method is "gravitational microlensing,"
where we wait for a MACHO to pass between us and a distant star, and
the gravity of the MACHO bends the starlight into two images.  These
images are too close together to resolve, but add up to more light, so
the star appears to brighten and then fade back to normal as the MACHO
passes by.  The shape is quite distinctive, and the brightening
happens only once so does not look like a variable star.  The
probability of such a close-enough approach is very low, so millions
of stars must be monitored to have a chance of finding these
events. The Large Magellanic Cloud is the most popular target.  A
number of groups---MACHO, EROS, OGLE, among others---have been doing
this for several years, and have found a number of good candidate
microlensing events.  At the moment, it is too early to say that
MACHOs have definitely been discovered, but it looks as though the
"brown dwarf" objects are just about excluded, while perhaps as much
as 50% of the dark matter could be in larger objects roughly 0.5 solar
masses, e.g., white dwarfs.

There is an axion search recently started at Lawrence Livermore Labs,
which uses a huge superconducting magnet to convert axions (if they
exist) into microwave photons.  For the big bang neutrinos, there is
currently no hope of detecting them because they have far less energy
than the well-known solar neutrinos (see FAQ entry E.01). However, if
a neutrino mass could be measured by lab experiments, we could
calculate their contribution to the dark matter.

For the supersymmetric particles, there are broadly three ways at
detecting them: i) Direct detection by watching a crystal down a deep
mine, and waiting for a WIMP to bounce off a nucleus in it with
observable results such as scintillation or heating of the crystal.
Very roughly 1 WIMP per day should hit each kg of detector, but the
tricky part is discriminating these from natural radioactivity.  The
WIMPS should have a preferred direction (due to the orbit of the Sun
around the galaxy), but we'll have to wait for next-generation
experiments to measure this.  ii) Indirect detection, whereby WIMPs
get captured in the Sun, and then a WIMP + anti-WIMP annihilate into
super-high energy (GeV) neutrinos which could be detected in huge
volume detectors, e.g., Antarctic ice or ocean water.  iii) Create
WIMPs directly at next-generation accelerators like LHC, measure their
properties and then calculate how many should have been produced in
the Big Bang.

With all these searches, there is a good chance that in the next 10
years or so we may find out what constitutes dark matter.

Further reading:

Astronomy magazine, Oct. 1996 issue contains many dark matter articles.

The Center for Particle Astrophysics home page at
<URL:http://physics7.berkeley.edu/> has several links including the
Question of Dark Matter page.

The MACHO home page at <URL:http://wwwmacho.mcmaster.ca/> has info on
the MACHO project and links to many other dark matter searches.

For cosmology background, see Ned Wright's Cosmology Tutorial at
<URL:http://www.astro.ucla.edu/~wright/cosmoall.htm>.

A more technical conference summary is at
<URL:http://xxx.lanl.gov/abs/astro-ph/9610003>.

Krauss, L., _The Fifth Essence_, Basic Books, NY 1989. 

Silk, J., _The Big Bang_, Freeman, San Francisco, 1988. 

Peebles, P.J.E., _Principles of Physical Cosmology_, Princeton, 1992
  (advanced)