Dark Matter makes up 85% of the mass of the Universe and it consists of a new particle that is not one of the 18 particles  that we have discovered. This means that we don't know what the majority of the Universe is made out of, which should strike you as remarkable.
Physicists of the world have a broad program searching for dark matter. One of the big challenges is that we don't know what dark matter is. This means that theoretical particle physicists must come up with ideas for how to directly discover this particle. Currently, the search for dark matter consists of a four pronged strategy
- Direct Production: The Large Hadron Collider(or other particle colliders) can in principle create the dark matter particle in the collisions. It will be seen by an apparent violation of conservation of energy/momentum because unseen particles will be flowing out of the detector. Discovering these new unseen particles won't prove that these particles are the majority of the mass of the Universe, but that there is a new stable particle that should be some component of the missing mass.
- Direct Detection: Dark matter is flying through the Earth all the time. We know that every three cubic centimeters in our part of the galaxy has the mass of one proton in it.  This means that there are three dark matter particles per cubic meter around the Earth, which means that 1,000,000 dark matter particles pour through our bodies every second. The vast majority of the time, the dark matter will go through undetected, but every now and again it can hit a nucleus and deposit a little bit of energy (unnoticeably small for us). This rare deposition of a microscopic quantity of energy is normally invisible unless you design a special detectors that can specifically measure it. Even if you design a special detector, one remaining difficulty is that lots energy rains down from the sky in the form of cosmic rays. To avoid cosmic rays, these detectors have to be placed deep underground (usually more than a mile beneath the surface of the Earth). We have roughly ten experiments searching for dark matter in this way.
- Indirect Detection Dark matter exists every where in the galaxy (and throughout the ambient Universe), but it is concentrated at the center of the galaxy. Dark matter can occasionally hit each other and annihilate. These annihilations result in very energetic cosmic rays being produced at the galactic center. We have telescopes designed to look for the remnants of these rare dark matter on dark matter collisions that come to us from the center of the galaxy. In fact, some physicists (including myself) are examining a striking feature that the Fermi Gamma Ray Space Telescope  observed emanating from the inner-most reaches of the galaxy that could be dark matter. We're waiting for confirmation from another experiment (hopefully in March). If this holds up to be true, then we might have already discovered dark matter.
- Axion Detection: The previous three types of experiments have looked for dark matter that is a heavy particle, but it is possible that dark matter might not be a normal massive particle, but instead a very light field and the dark matter are oscillations of this field (kind of like a Bose-Einstein condensate). We're looking for a special type of dark matter because it creates a magnetic field to create an alternating voltage that can be used to drive a current. Yes, dark matter can be a source of energy (a very, very small one). Unfortunately, because it's such a small source of energy, we have to amplify it a lot, which (if you recall your LRC circuits) means that you have to carefully scan through frequencies to listen to hear the dark matter of the Universe ringing at a special frequency - the Compton frequency of the particle. We would be tuning into the the cosmos singing.
Because we don't know what dark matter is, new ways of searching for dark matter are being constantly proposed . Because the above strategy is so good, frequently it requires simply reanalyzing the data in a new way to discover these new models. However, every now and again, there is a very novel theory of dark matter that requires searching for dark matter in a new way.
 The eighteen particles are six quarks (up, down, charm, strange, top, bottom), six leptons (electron, muon, tau, electron neutrino, muon neutrino, tau neutrino), the photon, W vector boson, Z vector boson, Higgs boson , the gluon and the graviton (which we've indirectly seen). 
 We don't know the mass of the dark matter, but many people suspect that it weighs approximately one hundred times as much a proton, so I'll use this number.
 The Fermi Gamma Ray Space Telescope is one of the "Great Observatories" that NASA launched with collaboration from the Department of Energy (United States), with the Hubble Space Telescope being the best known of these observatories. The Fermi Gamma Ray Space Telescope looks at the most energetic light shining on the Earth, Gamma Rays.
 See Physics: Assuming that Dark Matter is a particle, what are the theoretically well motivated Dark Matter particle candidates?
 Since the question details mention this, the Higgs Boson, starts off its life as a tachyon. A tachyon is an imaginary mass particle/field . Particles have their own internal clock that spins at the Compton frequency. The quantum mechanical wave function of particles goes like exp( i m c^2 t/ hbar) , since exp(2 pi i) =1, this returns to the same value after t = hbar/mc^2. When a tachyon comes along, this clock, goes from spinning around to being a growing exponential: i.e. it explodes! This happens to the Higgs boson in the early Universe, which causes the "electroweak phase transition." We're looking for gravity waves from this explosion and in my opinion, this would be the coolest thing to arise from Laser Interferometer Gravitational-wave Observatory (LIGO). How violent the electroweak phase transition is depends on the Higgs mass and to see the gravity waves, you want a violent transition; however, the current Higgs mass makes it look like the transition isn't particularly violent (it may even be smooth).
 Counting of particles is tricky, so if you hear someone say a different number (including myself), it isn't necessarily wrong, just a different way of counting. For instance, someone might legitimately say that there are eight gluons.
 Technically the mass squared is negative, so there are both positive and negative imaginary mass particles that are antiparticles of each other.
 This is the relativistic generalization of the quantum mechanical statement that wave functions are proportional to exp( i E t/hbar), where E= mc^2.More questions on Particle Physics:
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