NOTE: I recommend reading Noldorin's answer first, for useful background information, and Matt's answer afterward if you want additional detail
Noldorin is right that there isn't a single event that you can look at and identify a Higgs boson. In fact, unless the theories are drastically wrong, the Higgs particle is unstable and it has an exceedingly short lifetime - so short that it won't even make it out of the empty space inside the detector! Even at the speed of light, it can only travel a microscopic distance before it decays into other particles. (If I can find some numeric predictions I'll edit that information in.) So we won't be able to detect a Higgs boson directly.
What scientists will be looking for are particular patterns of known particles that are signatures of Higgs decay. For example, the standard model predicts that a Higgs boson could decay into two Z bosons, which in turn decay into a muon and antimuon each. So if physicists see that a particular collision produces two muons and two antimuons, among other particles, there's a chance that somewhere in the mess of particles produced in that collision, there was a Higgs boson. This is just one example, of course; there are many other sets of particles that the Higgs could decay into, and the large detectors at the LHC are designed to look for all of them.
Of course, Higgs decay is not the only thing that could produce two muon-antimuon pairs, and the same is true for other possible decay products. So just seeing the expected decay products is not a sure sign of a Higgs detection. The real evidence is going to come from the results of many collisions (billions or trillions), accumulated over time.
For each possible set of decay products, you can plot the fraction of collisions in which those decay products are produced (or rather, the scattering cross section, a related quantity) against the total energy of the particles coming into the collision. If the Higgs is real, you'll see a spike, called a resonance, in the graph at the energy corresponding to the mass of the Higgs particle. It'll look something like this plot, which was produced for the Z boson (which has a mass of only 91 GeV):
The image is from http://blogs.uslhc.us/the-z-boson-and-resonances, which is actually a pretty good read.
Anyway, to sum up: the main signature of the Higgs boson, like other unstable particles, will be this resonance peak that appears in a graph produced by aggregating data from many billions or trillions of collisions. Hopefully this makes it a bit clearer why there's going to be a lot of detailed analysis involved before we get any clear detection or non-detection of the Higgs particle.