Basically they have to rule out very masses by proving that they can't see them. experiments at LEP and the Tevatron have put the mass limits between 114 and ~200Gev.

All the standard model higgs (where it's just a higgs boson with no other weird physics) decay into two particles. It depends on the mass of the higgs what these decays are - for instance i'm studying 165Gev which is roughly 2 times the W mass, so in this region this is by far the most likely decay.

So far they've not seen this above the background and the more data they have, the more they can rule it out. The LHC will provide more data at the low (~114) region, where the main decays are b/bbar quarks, photons, tau lepton, c/cbar quarks and two gluons. All of these occur anyway in the detector so it's hard to spot - which is why there has been the least work in this region so far, and why ruling out the less likely WW and ZZ decays has been easier. Although it's the decay that occurs the least, the photon decay is the easiest to spot.

If they don't find the Higgs at any of these energies, it means it's not just a standard model one - i.e. it behaves not just by the laws we already know, but by new physics we've never seen. Supersymmetry and Extra Dimensions are two of the more prominent theories why the Higgs may not be in the standard model region.