For more information:
Electromagnetic Calorimeter: This device measures the total energy of e+, e-, and photons. These particles produce showers of e+/e- pairs in the material. The e-'s (or e+'s) are deflected by the electric fields of atoms, causing them to radiate photons. The photons then make e-/e+ pairs, which then radiate photons, etc. The number of final e+, e- pairs is proportional to the energy of the initiating particle.
Hadron Calorimeter: This device measures the total energy of hadrons. The hadrons interact with the dense material in this region, producing a shower of charged particles. The energy that these charged particles deposit is then measured.
Muon Chambers: Only muons and neutrinos get this far. The muons are detected, but the weakly interacting neutrinos escape. The presence of neutrinos can be inferred by the "missing" energy.
Magnet: The path of a charged particle curves in a magnetic field. The radius of curvature and direction tell the momentum and the sign of the charge.