The “average” collision isn’t that interesting from the point of view of new physics – most collisions will have 10-100 particles created from the remnants of the proton, which will generally fly off in all directions.
Rarely there will be a more interesting collision in which a much more energetic particle or group of particles is emitted in a particular direction from the collision. This is the sign that something happened in that particular interaction. Since there are a lot of collisions (200000000 per second!) there is a computer that filters out the boring collisions and records the details of the interesting ones.
From the interesting collisions we then look for patterns – sometimes we cluster the particles together (we call this a “jet”), which is a good indication that there was a high energy quark or gluon produced. Sometimes we look for individual electrons or muons. Then we can test for a particular signal, for example a Higgs decay, by determining if those jets or whatever would have the correct mass (when combined) to have come from a Higgs.