An event with a Z0 particle that decays into two electrons is recognised by that it only has two tracks which both point to signals in the electromagnetic calorimeter. Decays into two muons are similar, with the difference that the two tracks points to signals (crosses) in the muon detector instead.
When a Z0 particle decays into two tau particles, the tau particles themselves are not detected, they instantly decays into other particles. These tau events can be recognised knowing that they should have 2, 4 or possibly 6 charged tracks (+ any number of neutral tracks).
A Z0 particle decaying into two quarks is seen as two jets of particles, one jet from each quark. Sometimes one or several gluons are created at an early stage. In this case each gluon will create an extra jet.
Finally, neutrino events do not leave any traces at all in the detector, since neutrinos can not be detected. This means that we do not know how many such decays have taken place.