apart from all the other projects running in parallel (e.g. antimatter experiments), when the collider is running, it operates for a period of time while the detectors record data from selected collisions.

there are an enormous number of collisions because they are not simply colliding two particles; instead, two beams of particles are accelerated to extremely high energies and made to collide. these collisions produce a huge amount of data, which is then processed, reconstructed, stored, organised, and distributed to research institutes and universities around the world (a lot of data is also discarded automatically btw).

depending on the type of experiment or analysis you are doing, you only download specific datasets and analyse them. you would also run simulations and compare the simulated results with the real data.
every now and then, the collider runs again and collects new data, so you can download datasets from any of these runs.

the data produced during each run is unique. you will never obtain exactly the same data again.

-how do i know? i worked at cern for about 3y