We usually get a good idea about what particles were produced, and what they decayed into by analysing the data from the detector. For example, we can get the path and momentum of charged particles by seeing how their path is curved by a magnetic field. We get most of the particles to deposit energy in our calorimeters, from which we can calculate their momentum. We know the possible ways particles decay, how long they need to decay from theorists. We can apply energy-momentum conservation. We can see from the path of particles where they split. We also know the mass of all the known particles with a very high accuracy. So we use all these ingredients to get a complete picture about the collision.
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